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

Important Questions on Functions

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>TS EAMCET 2018 (04-May Shift-1)>Q 13

Let $f:R\to R, g:R\to R$ be differentiable functions such that $\left(fog\right)\left(x\right)=x$. If $f\left(x\right)=2x+\cos x+{\sin }^{2}x$, then the value of $\sum _{n=1}^{99}g\left(1+\left(2n-1\right)\pi \right)$ is

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>TS EAMCET 2018 (04-May Shift-1)>Q 14

If $f:[1,\infty )\to \left[1,\infty \right]$ is defined by $f\left(x\right)=\frac{1+\sqrt{1+4{\log }_{2}x}}{2}$, then $f^{-1}\left(3\right)=$

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>TS EAMCET 2019 (03-May Shift-2)>Q 15

Let $f\left(x\right)=(x+1{)}^2-1, x\ge -1.$ Then $\left\{x\mid f\left(x\right)=f^{-1}\left(x\right)\right\}=$

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>TS EAMCET 2021 (04-Aug Shift-2)>Q 16

Let $f: A\to B, g:B\to A$ be defined as $f\left(x\right)=x^2\forall x\in A$ and $g\left(x\right)=x^{1/2}\forall x\in B$. $f\left(x\right)$ and $g\left(x\right)$ are inverse functions to each other when