117312
Let \(f:(2, \infty) \rightarrow I R\) be the function defined by \(f(x)=x^2-4 x+5\). then, the range of \(f\) is
1 IR
2 \([1, \infty)\)
3 \([4, \infty]\)
4 \([5, \infty]\)
Explanation:
B Given, \(f:(2, \infty) \rightarrow \text { IR }\) \(f(x)=x^2-4 x+5\) \(f(x)=x^2-4 x+4+1\) \(f(x)=(x-2)^2+1\)Range of \(f(x)=[1, \infty)\)
JCECE-2018
Sets, Relation and Function
117320
The domain of the real function \(f(x)=\) \(\frac{1}{\sqrt{4-x^2}}\) is
1 the set of all real numbers
2 the set of all positive
3 \((-2,2)\)
4 \([-2,2]\)
Explanation:
C Given, \(f(x)=\frac{1}{\sqrt{4-x^2}}\) \(4-x^2>0\) \(x^2\lt 4\) \(-2\lt x\lt 2\)Domain \((-2,2)\).
BCECE-2012
Sets, Relation and Function
117341
The domain of \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) is.....
1 \((1,4)\)
2 \([1,4)\)
3 \((1,4]\)
4 \([1,4]\)
Explanation:
B Let \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) For domain of \(\log _{10}(4-\mathrm{x})\) \(\Rightarrow 4-x>0 \Rightarrow x\lt 4\) For domain of \(\cos ^{-1}\left(\frac{x-3}{2}\right) \Rightarrow-1 \leq \frac{x-3}{2} \leq 1\) \(\Rightarrow 1 \leq x \leq 5\)Now domain of \(f(\mathrm{x})\) will be \(\mathrm{x} \in[1,4)\)
Shift-I
Sets, Relation and Function
117351
The set of all real values of \(x\) for which the real valued function \(f(x)=\left(1+\frac{1}{x}\right)^x\) is defined, is
117312
Let \(f:(2, \infty) \rightarrow I R\) be the function defined by \(f(x)=x^2-4 x+5\). then, the range of \(f\) is
1 IR
2 \([1, \infty)\)
3 \([4, \infty]\)
4 \([5, \infty]\)
Explanation:
B Given, \(f:(2, \infty) \rightarrow \text { IR }\) \(f(x)=x^2-4 x+5\) \(f(x)=x^2-4 x+4+1\) \(f(x)=(x-2)^2+1\)Range of \(f(x)=[1, \infty)\)
JCECE-2018
Sets, Relation and Function
117320
The domain of the real function \(f(x)=\) \(\frac{1}{\sqrt{4-x^2}}\) is
1 the set of all real numbers
2 the set of all positive
3 \((-2,2)\)
4 \([-2,2]\)
Explanation:
C Given, \(f(x)=\frac{1}{\sqrt{4-x^2}}\) \(4-x^2>0\) \(x^2\lt 4\) \(-2\lt x\lt 2\)Domain \((-2,2)\).
BCECE-2012
Sets, Relation and Function
117341
The domain of \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) is.....
1 \((1,4)\)
2 \([1,4)\)
3 \((1,4]\)
4 \([1,4]\)
Explanation:
B Let \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) For domain of \(\log _{10}(4-\mathrm{x})\) \(\Rightarrow 4-x>0 \Rightarrow x\lt 4\) For domain of \(\cos ^{-1}\left(\frac{x-3}{2}\right) \Rightarrow-1 \leq \frac{x-3}{2} \leq 1\) \(\Rightarrow 1 \leq x \leq 5\)Now domain of \(f(\mathrm{x})\) will be \(\mathrm{x} \in[1,4)\)
Shift-I
Sets, Relation and Function
117351
The set of all real values of \(x\) for which the real valued function \(f(x)=\left(1+\frac{1}{x}\right)^x\) is defined, is
117312
Let \(f:(2, \infty) \rightarrow I R\) be the function defined by \(f(x)=x^2-4 x+5\). then, the range of \(f\) is
1 IR
2 \([1, \infty)\)
3 \([4, \infty]\)
4 \([5, \infty]\)
Explanation:
B Given, \(f:(2, \infty) \rightarrow \text { IR }\) \(f(x)=x^2-4 x+5\) \(f(x)=x^2-4 x+4+1\) \(f(x)=(x-2)^2+1\)Range of \(f(x)=[1, \infty)\)
JCECE-2018
Sets, Relation and Function
117320
The domain of the real function \(f(x)=\) \(\frac{1}{\sqrt{4-x^2}}\) is
1 the set of all real numbers
2 the set of all positive
3 \((-2,2)\)
4 \([-2,2]\)
Explanation:
C Given, \(f(x)=\frac{1}{\sqrt{4-x^2}}\) \(4-x^2>0\) \(x^2\lt 4\) \(-2\lt x\lt 2\)Domain \((-2,2)\).
BCECE-2012
Sets, Relation and Function
117341
The domain of \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) is.....
1 \((1,4)\)
2 \([1,4)\)
3 \((1,4]\)
4 \([1,4]\)
Explanation:
B Let \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) For domain of \(\log _{10}(4-\mathrm{x})\) \(\Rightarrow 4-x>0 \Rightarrow x\lt 4\) For domain of \(\cos ^{-1}\left(\frac{x-3}{2}\right) \Rightarrow-1 \leq \frac{x-3}{2} \leq 1\) \(\Rightarrow 1 \leq x \leq 5\)Now domain of \(f(\mathrm{x})\) will be \(\mathrm{x} \in[1,4)\)
Shift-I
Sets, Relation and Function
117351
The set of all real values of \(x\) for which the real valued function \(f(x)=\left(1+\frac{1}{x}\right)^x\) is defined, is
117312
Let \(f:(2, \infty) \rightarrow I R\) be the function defined by \(f(x)=x^2-4 x+5\). then, the range of \(f\) is
1 IR
2 \([1, \infty)\)
3 \([4, \infty]\)
4 \([5, \infty]\)
Explanation:
B Given, \(f:(2, \infty) \rightarrow \text { IR }\) \(f(x)=x^2-4 x+5\) \(f(x)=x^2-4 x+4+1\) \(f(x)=(x-2)^2+1\)Range of \(f(x)=[1, \infty)\)
JCECE-2018
Sets, Relation and Function
117320
The domain of the real function \(f(x)=\) \(\frac{1}{\sqrt{4-x^2}}\) is
1 the set of all real numbers
2 the set of all positive
3 \((-2,2)\)
4 \([-2,2]\)
Explanation:
C Given, \(f(x)=\frac{1}{\sqrt{4-x^2}}\) \(4-x^2>0\) \(x^2\lt 4\) \(-2\lt x\lt 2\)Domain \((-2,2)\).
BCECE-2012
Sets, Relation and Function
117341
The domain of \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) is.....
1 \((1,4)\)
2 \([1,4)\)
3 \((1,4]\)
4 \([1,4]\)
Explanation:
B Let \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) For domain of \(\log _{10}(4-\mathrm{x})\) \(\Rightarrow 4-x>0 \Rightarrow x\lt 4\) For domain of \(\cos ^{-1}\left(\frac{x-3}{2}\right) \Rightarrow-1 \leq \frac{x-3}{2} \leq 1\) \(\Rightarrow 1 \leq x \leq 5\)Now domain of \(f(\mathrm{x})\) will be \(\mathrm{x} \in[1,4)\)
Shift-I
Sets, Relation and Function
117351
The set of all real values of \(x\) for which the real valued function \(f(x)=\left(1+\frac{1}{x}\right)^x\) is defined, is
117312
Let \(f:(2, \infty) \rightarrow I R\) be the function defined by \(f(x)=x^2-4 x+5\). then, the range of \(f\) is
1 IR
2 \([1, \infty)\)
3 \([4, \infty]\)
4 \([5, \infty]\)
Explanation:
B Given, \(f:(2, \infty) \rightarrow \text { IR }\) \(f(x)=x^2-4 x+5\) \(f(x)=x^2-4 x+4+1\) \(f(x)=(x-2)^2+1\)Range of \(f(x)=[1, \infty)\)
JCECE-2018
Sets, Relation and Function
117320
The domain of the real function \(f(x)=\) \(\frac{1}{\sqrt{4-x^2}}\) is
1 the set of all real numbers
2 the set of all positive
3 \((-2,2)\)
4 \([-2,2]\)
Explanation:
C Given, \(f(x)=\frac{1}{\sqrt{4-x^2}}\) \(4-x^2>0\) \(x^2\lt 4\) \(-2\lt x\lt 2\)Domain \((-2,2)\).
BCECE-2012
Sets, Relation and Function
117341
The domain of \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) is.....
1 \((1,4)\)
2 \([1,4)\)
3 \((1,4]\)
4 \([1,4]\)
Explanation:
B Let \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) For domain of \(\log _{10}(4-\mathrm{x})\) \(\Rightarrow 4-x>0 \Rightarrow x\lt 4\) For domain of \(\cos ^{-1}\left(\frac{x-3}{2}\right) \Rightarrow-1 \leq \frac{x-3}{2} \leq 1\) \(\Rightarrow 1 \leq x \leq 5\)Now domain of \(f(\mathrm{x})\) will be \(\mathrm{x} \in[1,4)\)
Shift-I
Sets, Relation and Function
117351
The set of all real values of \(x\) for which the real valued function \(f(x)=\left(1+\frac{1}{x}\right)^x\) is defined, is