Domain, Co-domain and Range of Function
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Sets, Relation and Function

117379 Given that \(a, b\) and \(c\) are real numbers such that \(b^2=4 a c\) and \(a>0\). The maximal possible set \(\mathrm{D} \subseteq \mathrm{R}\) on which the function \(f: \mathrm{D} \rightarrow \mathrm{R}\) given by
\(f(x)=\log \left\{a x^3+(a+b) x^2+(b+c) x+c\right\}\) is defined, is

1 \(\mathrm{R}-\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\}\)
2 \(\mathrm{R}-\left(\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\} \cup(-\infty,-1)\right)\)
3 \(\mathrm{R}-\left(\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\} \cup\{\mathrm{x}: \mathrm{x} \geq 1\}\right)\)
4 \(\mathrm{R}-(\{-\mathrm{b} / 2 \mathrm{a}\} \cup(-\infty,-1])\)
Shift-I
Sets, Relation and Function

117380 Solve \((8-t)^2\lt \left(t^2-3 t-10\right)\)

1 \(\left(\frac{74}{13}, 8\right]\)
2 \(\left(\frac{74}{13}, \infty\right)\)
3 \((\infty, 8)\)
4 \((8, \infty]\)
Shift-II
Sets, Relation and Function

117381 The domain of \(\sqrt{|x|-x}\) is

1 \((-\infty 0)\)
2 \((0, \infty)\)
3 \((-\infty, \infty)\)
4 \((\mathrm{R}-(0)\)
Shift-II
Sets, Relation and Function

117382 Let \(f(x)=\sqrt{x^2-3 x+2}\) and \(g(x)=\sqrt{x}\) be two given functions. If \(S\) be the domain of fog and \(T\) be the domain of gof, then

1 \(\mathrm{S}=\mathrm{T}\)
2 \(\mathrm{S} \cap \mathrm{T}=\phi\)
3 \(\mathrm{S} \cap \mathrm{T}\) is a singleton
4 \(\mathrm{S} \cap \mathrm{T}\) is aninterval
WB JEE-2020
Sets, Relation and Function

117383 The domain of \(f(x)=\sqrt{\left(\frac{1}{\sqrt{x}}-\sqrt{(x+1)}\right)}\) is

1 \(x>-1\)
2 \((-1, \infty) \backslash\{0\}\)
3 \(\left(0, \frac{\sqrt{5}-1}{2}\right]\)
4 \(\left[\frac{1-\sqrt{5}}{2}, 0\right)\)
WB JEE-2020
NEET DIGITAL LIBRARY
Sets, Relation and Function

117379 Given that \(a, b\) and \(c\) are real numbers such that \(b^2=4 a c\) and \(a>0\). The maximal possible set \(\mathrm{D} \subseteq \mathrm{R}\) on which the function \(f: \mathrm{D} \rightarrow \mathrm{R}\) given by
\(f(x)=\log \left\{a x^3+(a+b) x^2+(b+c) x+c\right\}\) is defined, is

1 \(\mathrm{R}-\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\}\)
2 \(\mathrm{R}-\left(\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\} \cup(-\infty,-1)\right)\)
3 \(\mathrm{R}-\left(\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\} \cup\{\mathrm{x}: \mathrm{x} \geq 1\}\right)\)
4 \(\mathrm{R}-(\{-\mathrm{b} / 2 \mathrm{a}\} \cup(-\infty,-1])\)
Shift-I
Sets, Relation and Function

117380 Solve \((8-t)^2\lt \left(t^2-3 t-10\right)\)

1 \(\left(\frac{74}{13}, 8\right]\)
2 \(\left(\frac{74}{13}, \infty\right)\)
3 \((\infty, 8)\)
4 \((8, \infty]\)
Shift-II
Sets, Relation and Function

117381 The domain of \(\sqrt{|x|-x}\) is

1 \((-\infty 0)\)
2 \((0, \infty)\)
3 \((-\infty, \infty)\)
4 \((\mathrm{R}-(0)\)
Shift-II
Sets, Relation and Function

117382 Let \(f(x)=\sqrt{x^2-3 x+2}\) and \(g(x)=\sqrt{x}\) be two given functions. If \(S\) be the domain of fog and \(T\) be the domain of gof, then

1 \(\mathrm{S}=\mathrm{T}\)
2 \(\mathrm{S} \cap \mathrm{T}=\phi\)
3 \(\mathrm{S} \cap \mathrm{T}\) is a singleton
4 \(\mathrm{S} \cap \mathrm{T}\) is aninterval
WB JEE-2020
Sets, Relation and Function

117383 The domain of \(f(x)=\sqrt{\left(\frac{1}{\sqrt{x}}-\sqrt{(x+1)}\right)}\) is

1 \(x>-1\)
2 \((-1, \infty) \backslash\{0\}\)
3 \(\left(0, \frac{\sqrt{5}-1}{2}\right]\)
4 \(\left[\frac{1-\sqrt{5}}{2}, 0\right)\)
WB JEE-2020
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Sets, Relation and Function

117379 Given that \(a, b\) and \(c\) are real numbers such that \(b^2=4 a c\) and \(a>0\). The maximal possible set \(\mathrm{D} \subseteq \mathrm{R}\) on which the function \(f: \mathrm{D} \rightarrow \mathrm{R}\) given by
\(f(x)=\log \left\{a x^3+(a+b) x^2+(b+c) x+c\right\}\) is defined, is

1 \(\mathrm{R}-\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\}\)
2 \(\mathrm{R}-\left(\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\} \cup(-\infty,-1)\right)\)
3 \(\mathrm{R}-\left(\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\} \cup\{\mathrm{x}: \mathrm{x} \geq 1\}\right)\)
4 \(\mathrm{R}-(\{-\mathrm{b} / 2 \mathrm{a}\} \cup(-\infty,-1])\)
Shift-I
Sets, Relation and Function

117380 Solve \((8-t)^2\lt \left(t^2-3 t-10\right)\)

1 \(\left(\frac{74}{13}, 8\right]\)
2 \(\left(\frac{74}{13}, \infty\right)\)
3 \((\infty, 8)\)
4 \((8, \infty]\)
Shift-II
Sets, Relation and Function

117381 The domain of \(\sqrt{|x|-x}\) is

1 \((-\infty 0)\)
2 \((0, \infty)\)
3 \((-\infty, \infty)\)
4 \((\mathrm{R}-(0)\)
Shift-II
Sets, Relation and Function

117382 Let \(f(x)=\sqrt{x^2-3 x+2}\) and \(g(x)=\sqrt{x}\) be two given functions. If \(S\) be the domain of fog and \(T\) be the domain of gof, then

1 \(\mathrm{S}=\mathrm{T}\)
2 \(\mathrm{S} \cap \mathrm{T}=\phi\)
3 \(\mathrm{S} \cap \mathrm{T}\) is a singleton
4 \(\mathrm{S} \cap \mathrm{T}\) is aninterval
WB JEE-2020
Sets, Relation and Function

117383 The domain of \(f(x)=\sqrt{\left(\frac{1}{\sqrt{x}}-\sqrt{(x+1)}\right)}\) is

1 \(x>-1\)
2 \((-1, \infty) \backslash\{0\}\)
3 \(\left(0, \frac{\sqrt{5}-1}{2}\right]\)
4 \(\left[\frac{1-\sqrt{5}}{2}, 0\right)\)
WB JEE-2020
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Sets, Relation and Function

117379 Given that \(a, b\) and \(c\) are real numbers such that \(b^2=4 a c\) and \(a>0\). The maximal possible set \(\mathrm{D} \subseteq \mathrm{R}\) on which the function \(f: \mathrm{D} \rightarrow \mathrm{R}\) given by
\(f(x)=\log \left\{a x^3+(a+b) x^2+(b+c) x+c\right\}\) is defined, is

1 \(\mathrm{R}-\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\}\)
2 \(\mathrm{R}-\left(\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\} \cup(-\infty,-1)\right)\)
3 \(\mathrm{R}-\left(\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\} \cup\{\mathrm{x}: \mathrm{x} \geq 1\}\right)\)
4 \(\mathrm{R}-(\{-\mathrm{b} / 2 \mathrm{a}\} \cup(-\infty,-1])\)
Shift-I
Sets, Relation and Function

117380 Solve \((8-t)^2\lt \left(t^2-3 t-10\right)\)

1 \(\left(\frac{74}{13}, 8\right]\)
2 \(\left(\frac{74}{13}, \infty\right)\)
3 \((\infty, 8)\)
4 \((8, \infty]\)
Shift-II
Sets, Relation and Function

117381 The domain of \(\sqrt{|x|-x}\) is

1 \((-\infty 0)\)
2 \((0, \infty)\)
3 \((-\infty, \infty)\)
4 \((\mathrm{R}-(0)\)
Shift-II
Sets, Relation and Function

117382 Let \(f(x)=\sqrt{x^2-3 x+2}\) and \(g(x)=\sqrt{x}\) be two given functions. If \(S\) be the domain of fog and \(T\) be the domain of gof, then

1 \(\mathrm{S}=\mathrm{T}\)
2 \(\mathrm{S} \cap \mathrm{T}=\phi\)
3 \(\mathrm{S} \cap \mathrm{T}\) is a singleton
4 \(\mathrm{S} \cap \mathrm{T}\) is aninterval
WB JEE-2020
Sets, Relation and Function

117383 The domain of \(f(x)=\sqrt{\left(\frac{1}{\sqrt{x}}-\sqrt{(x+1)}\right)}\) is

1 \(x>-1\)
2 \((-1, \infty) \backslash\{0\}\)
3 \(\left(0, \frac{\sqrt{5}-1}{2}\right]\)
4 \(\left[\frac{1-\sqrt{5}}{2}, 0\right)\)
WB JEE-2020
NEET DIGITAL LIBRARY
Sets, Relation and Function

117379 Given that \(a, b\) and \(c\) are real numbers such that \(b^2=4 a c\) and \(a>0\). The maximal possible set \(\mathrm{D} \subseteq \mathrm{R}\) on which the function \(f: \mathrm{D} \rightarrow \mathrm{R}\) given by
\(f(x)=\log \left\{a x^3+(a+b) x^2+(b+c) x+c\right\}\) is defined, is

1 \(\mathrm{R}-\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\}\)
2 \(\mathrm{R}-\left(\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\} \cup(-\infty,-1)\right)\)
3 \(\mathrm{R}-\left(\left\{-\frac{\mathrm{b}}{2 \mathrm{a}}\right\} \cup\{\mathrm{x}: \mathrm{x} \geq 1\}\right)\)
4 \(\mathrm{R}-(\{-\mathrm{b} / 2 \mathrm{a}\} \cup(-\infty,-1])\)
Shift-I
Sets, Relation and Function

117380 Solve \((8-t)^2\lt \left(t^2-3 t-10\right)\)

1 \(\left(\frac{74}{13}, 8\right]\)
2 \(\left(\frac{74}{13}, \infty\right)\)
3 \((\infty, 8)\)
4 \((8, \infty]\)
Shift-II
Sets, Relation and Function

117381 The domain of \(\sqrt{|x|-x}\) is

1 \((-\infty 0)\)
2 \((0, \infty)\)
3 \((-\infty, \infty)\)
4 \((\mathrm{R}-(0)\)
Shift-II
Sets, Relation and Function

117382 Let \(f(x)=\sqrt{x^2-3 x+2}\) and \(g(x)=\sqrt{x}\) be two given functions. If \(S\) be the domain of fog and \(T\) be the domain of gof, then

1 \(\mathrm{S}=\mathrm{T}\)
2 \(\mathrm{S} \cap \mathrm{T}=\phi\)
3 \(\mathrm{S} \cap \mathrm{T}\) is a singleton
4 \(\mathrm{S} \cap \mathrm{T}\) is aninterval
WB JEE-2020
Sets, Relation and Function

117383 The domain of \(f(x)=\sqrt{\left(\frac{1}{\sqrt{x}}-\sqrt{(x+1)}\right)}\) is

1 \(x>-1\)
2 \((-1, \infty) \backslash\{0\}\)
3 \(\left(0, \frac{\sqrt{5}-1}{2}\right]\)
4 \(\left[\frac{1-\sqrt{5}}{2}, 0\right)\)
WB JEE-2020