Properties of Functions and Graphs
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NEET DIGITAL LIBRARY
Sets, Relation and Function

116961 The even function of the following is

1 \(f(x)=\frac{a^x+a^{-x}}{a^x-a^{-x}}\)
2 \(f(x)=\frac{a^x+1}{a^x-1}\)
3 \(f(x)=x \cdot \frac{a^x-1}{a^x+1}\)
4 \(f(x)=\log _2\left(x+\sqrt{x^2+1}\right)\)
WB JEE-2011
Sets, Relation and Function

116967 If \(\left(a^4-2 a^2 b^2+b^4\right)^{x-1}=(a-b)^{2 x}(a+b)^{-2}, a>0 b\) \(>0\), then \(\mathrm{x}=\)

1 \(\frac{\log \mathrm{a}}{\log \mathrm{b}}\)
2 \(\frac{\log \mathrm{b}}{\log \mathrm{a}}\)
3 \(\frac{\log (a+b)}{\log |a-b|}\)
4 \(\frac{\log |a-b|}{\log (a+b)}\)
COMEDK-2018
Sets, Relation and Function

116968 If (4) \()_9^{\log _9 3}+(9)^{\log _2 4}=(10)^{\log _x 83}\), then \(x\) is equal to

1 10
2 4
3 -10
4 -4
COMEDK-2012
Sets, Relation and Function

117029 If [] denotes the greatest integer function, then
\(f(\mathbf{x})=[\mathbf{x}]+\left[\mathbf{x}+\frac{\mathbf{1}}{\mathbf{2}}\right]\)

1 is continuous at \(x=\frac{1}{2}\)
2 is discontinuous at \(x=\frac{1}{2}\)
3 \(\lim _{\mathrm{x} \rightarrow(1 / 2)^{+}} f(\mathrm{x})=2\)
4 \(\lim _{\mathrm{x} \rightarrow(1 / 2)^{-}} f(\mathrm{x})=1\)
Manipal UGET-2015
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Sets, Relation and Function

116961 The even function of the following is

1 \(f(x)=\frac{a^x+a^{-x}}{a^x-a^{-x}}\)
2 \(f(x)=\frac{a^x+1}{a^x-1}\)
3 \(f(x)=x \cdot \frac{a^x-1}{a^x+1}\)
4 \(f(x)=\log _2\left(x+\sqrt{x^2+1}\right)\)
WB JEE-2011
Sets, Relation and Function

116967 If \(\left(a^4-2 a^2 b^2+b^4\right)^{x-1}=(a-b)^{2 x}(a+b)^{-2}, a>0 b\) \(>0\), then \(\mathrm{x}=\)

1 \(\frac{\log \mathrm{a}}{\log \mathrm{b}}\)
2 \(\frac{\log \mathrm{b}}{\log \mathrm{a}}\)
3 \(\frac{\log (a+b)}{\log |a-b|}\)
4 \(\frac{\log |a-b|}{\log (a+b)}\)
COMEDK-2018
Sets, Relation and Function

116968 If (4) \()_9^{\log _9 3}+(9)^{\log _2 4}=(10)^{\log _x 83}\), then \(x\) is equal to

1 10
2 4
3 -10
4 -4
COMEDK-2012
Sets, Relation and Function

117029 If [] denotes the greatest integer function, then
\(f(\mathbf{x})=[\mathbf{x}]+\left[\mathbf{x}+\frac{\mathbf{1}}{\mathbf{2}}\right]\)

1 is continuous at \(x=\frac{1}{2}\)
2 is discontinuous at \(x=\frac{1}{2}\)
3 \(\lim _{\mathrm{x} \rightarrow(1 / 2)^{+}} f(\mathrm{x})=2\)
4 \(\lim _{\mathrm{x} \rightarrow(1 / 2)^{-}} f(\mathrm{x})=1\)
Manipal UGET-2015
For More Updates join with Us
Sets, Relation and Function

116961 The even function of the following is

1 \(f(x)=\frac{a^x+a^{-x}}{a^x-a^{-x}}\)
2 \(f(x)=\frac{a^x+1}{a^x-1}\)
3 \(f(x)=x \cdot \frac{a^x-1}{a^x+1}\)
4 \(f(x)=\log _2\left(x+\sqrt{x^2+1}\right)\)
WB JEE-2011
Sets, Relation and Function

116967 If \(\left(a^4-2 a^2 b^2+b^4\right)^{x-1}=(a-b)^{2 x}(a+b)^{-2}, a>0 b\) \(>0\), then \(\mathrm{x}=\)

1 \(\frac{\log \mathrm{a}}{\log \mathrm{b}}\)
2 \(\frac{\log \mathrm{b}}{\log \mathrm{a}}\)
3 \(\frac{\log (a+b)}{\log |a-b|}\)
4 \(\frac{\log |a-b|}{\log (a+b)}\)
COMEDK-2018
Sets, Relation and Function

116968 If (4) \()_9^{\log _9 3}+(9)^{\log _2 4}=(10)^{\log _x 83}\), then \(x\) is equal to

1 10
2 4
3 -10
4 -4
COMEDK-2012
Sets, Relation and Function

117029 If [] denotes the greatest integer function, then
\(f(\mathbf{x})=[\mathbf{x}]+\left[\mathbf{x}+\frac{\mathbf{1}}{\mathbf{2}}\right]\)

1 is continuous at \(x=\frac{1}{2}\)
2 is discontinuous at \(x=\frac{1}{2}\)
3 \(\lim _{\mathrm{x} \rightarrow(1 / 2)^{+}} f(\mathrm{x})=2\)
4 \(\lim _{\mathrm{x} \rightarrow(1 / 2)^{-}} f(\mathrm{x})=1\)
Manipal UGET-2015
NEET DIGITAL LIBRARY
Sets, Relation and Function

116961 The even function of the following is

1 \(f(x)=\frac{a^x+a^{-x}}{a^x-a^{-x}}\)
2 \(f(x)=\frac{a^x+1}{a^x-1}\)
3 \(f(x)=x \cdot \frac{a^x-1}{a^x+1}\)
4 \(f(x)=\log _2\left(x+\sqrt{x^2+1}\right)\)
WB JEE-2011
Sets, Relation and Function

116967 If \(\left(a^4-2 a^2 b^2+b^4\right)^{x-1}=(a-b)^{2 x}(a+b)^{-2}, a>0 b\) \(>0\), then \(\mathrm{x}=\)

1 \(\frac{\log \mathrm{a}}{\log \mathrm{b}}\)
2 \(\frac{\log \mathrm{b}}{\log \mathrm{a}}\)
3 \(\frac{\log (a+b)}{\log |a-b|}\)
4 \(\frac{\log |a-b|}{\log (a+b)}\)
COMEDK-2018
Sets, Relation and Function

116968 If (4) \()_9^{\log _9 3}+(9)^{\log _2 4}=(10)^{\log _x 83}\), then \(x\) is equal to

1 10
2 4
3 -10
4 -4
COMEDK-2012
Sets, Relation and Function

117029 If [] denotes the greatest integer function, then
\(f(\mathbf{x})=[\mathbf{x}]+\left[\mathbf{x}+\frac{\mathbf{1}}{\mathbf{2}}\right]\)

1 is continuous at \(x=\frac{1}{2}\)
2 is discontinuous at \(x=\frac{1}{2}\)
3 \(\lim _{\mathrm{x} \rightarrow(1 / 2)^{+}} f(\mathrm{x})=2\)
4 \(\lim _{\mathrm{x} \rightarrow(1 / 2)^{-}} f(\mathrm{x})=1\)
Manipal UGET-2015
Join With Us for More Updates