Properties of Functions and Graphs
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Sets, Relation and Function

116915 If \(f(x)=\frac{1-x}{1+x}, x \neq 0,-1\) and \(\alpha=f(f(x))+f(f(1 / x))\), then

1 \(\alpha>2\)
2 \(\alpha\lt -2\)
3 \(|\alpha|>2\)
4 \(\alpha=2\)
JCECE-2015
Sets, Relation and Function

116916 The function \(f(x)=\log \left(x+\sqrt{x^2+1}\right)\) is:

1 even function
2 odd function
3 neither even nor odd
4 periodic function
BCECE-2006
Sets, Relation and Function

116917 If \(f(x)=\left(\frac{1}{x}\right)^x\), then the maximum value of \(f(x)\) is:

1 e
2 \((\mathrm{e})^{1 / \mathrm{e}}\)
3 \(\left(\frac{1}{\mathrm{e}}\right)^{\mathrm{e}}\)
4 none of these
JCECE-2004
Sets, Relation and Function

116918 If \(f(x)=\log \left(\frac{1+x}{1-x}\right)\), then \(f\left(\frac{2 x}{1+x^2}\right)\) will be equal to:

1 \(2 \mathrm{f}\left(\mathrm{x}^2\right)\)
2 \(f\left(x^2\right)\)
3 \(2 \mathrm{f}(2 \mathrm{x})\)
4 \(2 \mathrm{f}(\mathrm{x})\)
JCECE-2004
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Sets, Relation and Function

116915 If \(f(x)=\frac{1-x}{1+x}, x \neq 0,-1\) and \(\alpha=f(f(x))+f(f(1 / x))\), then

1 \(\alpha>2\)
2 \(\alpha\lt -2\)
3 \(|\alpha|>2\)
4 \(\alpha=2\)
JCECE-2015
Sets, Relation and Function

116916 The function \(f(x)=\log \left(x+\sqrt{x^2+1}\right)\) is:

1 even function
2 odd function
3 neither even nor odd
4 periodic function
BCECE-2006
Sets, Relation and Function

116917 If \(f(x)=\left(\frac{1}{x}\right)^x\), then the maximum value of \(f(x)\) is:

1 e
2 \((\mathrm{e})^{1 / \mathrm{e}}\)
3 \(\left(\frac{1}{\mathrm{e}}\right)^{\mathrm{e}}\)
4 none of these
JCECE-2004
Sets, Relation and Function

116918 If \(f(x)=\log \left(\frac{1+x}{1-x}\right)\), then \(f\left(\frac{2 x}{1+x^2}\right)\) will be equal to:

1 \(2 \mathrm{f}\left(\mathrm{x}^2\right)\)
2 \(f\left(x^2\right)\)
3 \(2 \mathrm{f}(2 \mathrm{x})\)
4 \(2 \mathrm{f}(\mathrm{x})\)
JCECE-2004
NEET DIGITAL LIBRARY
Sets, Relation and Function

116915 If \(f(x)=\frac{1-x}{1+x}, x \neq 0,-1\) and \(\alpha=f(f(x))+f(f(1 / x))\), then

1 \(\alpha>2\)
2 \(\alpha\lt -2\)
3 \(|\alpha|>2\)
4 \(\alpha=2\)
JCECE-2015
Sets, Relation and Function

116916 The function \(f(x)=\log \left(x+\sqrt{x^2+1}\right)\) is:

1 even function
2 odd function
3 neither even nor odd
4 periodic function
BCECE-2006
Sets, Relation and Function

116917 If \(f(x)=\left(\frac{1}{x}\right)^x\), then the maximum value of \(f(x)\) is:

1 e
2 \((\mathrm{e})^{1 / \mathrm{e}}\)
3 \(\left(\frac{1}{\mathrm{e}}\right)^{\mathrm{e}}\)
4 none of these
JCECE-2004
Sets, Relation and Function

116918 If \(f(x)=\log \left(\frac{1+x}{1-x}\right)\), then \(f\left(\frac{2 x}{1+x^2}\right)\) will be equal to:

1 \(2 \mathrm{f}\left(\mathrm{x}^2\right)\)
2 \(f\left(x^2\right)\)
3 \(2 \mathrm{f}(2 \mathrm{x})\)
4 \(2 \mathrm{f}(\mathrm{x})\)
JCECE-2004
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Sets, Relation and Function

116915 If \(f(x)=\frac{1-x}{1+x}, x \neq 0,-1\) and \(\alpha=f(f(x))+f(f(1 / x))\), then

1 \(\alpha>2\)
2 \(\alpha\lt -2\)
3 \(|\alpha|>2\)
4 \(\alpha=2\)
JCECE-2015
Sets, Relation and Function

116916 The function \(f(x)=\log \left(x+\sqrt{x^2+1}\right)\) is:

1 even function
2 odd function
3 neither even nor odd
4 periodic function
BCECE-2006
Sets, Relation and Function

116917 If \(f(x)=\left(\frac{1}{x}\right)^x\), then the maximum value of \(f(x)\) is:

1 e
2 \((\mathrm{e})^{1 / \mathrm{e}}\)
3 \(\left(\frac{1}{\mathrm{e}}\right)^{\mathrm{e}}\)
4 none of these
JCECE-2004
Sets, Relation and Function

116918 If \(f(x)=\log \left(\frac{1+x}{1-x}\right)\), then \(f\left(\frac{2 x}{1+x^2}\right)\) will be equal to:

1 \(2 \mathrm{f}\left(\mathrm{x}^2\right)\)
2 \(f\left(x^2\right)\)
3 \(2 \mathrm{f}(2 \mathrm{x})\)
4 \(2 \mathrm{f}(\mathrm{x})\)
JCECE-2004
For More Updates join with Us