Find the range of $\mathrm{f}\left(\mathrm{x}\right)=\frac{{\mathrm{x}}^2-2}{{\mathrm{x}}^2-3}$ :

Important Questions on Functions and Graphs

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 17 - SNAP>CMAT>Q 30

If $\mathrm{f}\left(\mathrm{x}\right)=\frac{{\mathrm{x}}^2+2\mathrm{x}+3}{\mathrm{x}}$, then the range of the function is

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 17 - SNAP>CMAT>Q 31

Which of the following pairs are identical :

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 17 - SNAP>CMAT>Q 32

If $\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\sqrt{\left|\mathrm{x}\right|-\mathrm{x}}}$ and $\mathrm{g}\left(\mathrm{x}\right)=\frac{1}{\sqrt{\mathrm{x}-\left|\mathrm{x}\right|}}$, then

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 17 - SNAP>CMAT>Q 33

If $\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x},\mathrm{g}\left(\mathrm{x}\right)=\sqrt{{\mathrm{x}}^2}$ and $\mathrm{h}\left(\mathrm{x}\right)=\frac{{\mathrm{x}}^2}{\mathrm{x}}$, then the set of values for which the given functions $\mathrm{f}\left(\mathrm{x}\right), \mathrm{g}\left(\mathrm{x}\right)$ and $\mathrm{h}\left(\mathrm{x}\right)$ are identical is :

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 17 - SNAP>CMAT>Q 35

If $\mathrm{f}\left(\mathrm{x}\right)=Sgn\mathrm{x}$ and $\mathrm{g}\left(\mathrm{x}\right)=1+\mathrm{x}-\left[\mathrm{x}\right]$. Then for all $x>0,$ $\mathrm{x}$ $\mathrm{f}\left(\mathrm{g}\right(\mathrm{x}\left)\right)$ is equal to :

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 17 - SNAP>CMAT>Q 36

If 64xand $\alpha ,\beta$ are the roots of $4\mathrm{x}+\frac{1}{\mathrm{x}}=2$, then:

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 17 - SNAP>CMAT>Q 37

If $\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{x}}{\sqrt{1+{\mathrm{x}}^2}}$, then $\mathrm{f}\left(\mathrm{f}\right(\mathrm{f}\left(\mathrm{x}\right)\left)\right)$ is :

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 17 - SNAP>CMAT>Q 38

If $\mathrm{f}\left(\mathrm{x}\right)=\frac{4^{\mathrm{x}}}{4^{\mathrm{x}}+2}$, then the value of $\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}(1-\mathrm{x})$ is :