Embibe Experts Solutions for Chapter: Functions, Exercise 1: AP EAPCET - 20 Aug 2021 Forenoon

The domain of the function $f\left(x\right)=\frac{1}{\left[x\right]-1}$, where $\left[x\right]$ is greatest integer function of $x$ is

If $f(10-x)=3x^2+4x-5$ and $f\left(x\right)=p{x}^2+qx+r$ then $p+q+r=$

Let $f:R\to R$ be a function defined by $f\left(x\right)=\frac{4^x}{4^x+2}$. what is the value of $f\left(\frac{1}{4}\right)+2f\left(\frac{1}{2}\right)+f\left(\frac{3}{4}\right)=$?

The real valued function $f\left(x\right)=\frac{x}{e^x-1}+\frac{x}{2}+1$ defined on $R\backslash \left\{0\right\}$ is

Let $f\left(x\right)=x^3$ and $g\left(x\right)=3^x$, then the quadratic equation whose roots are solutions of the equation $(f\circ g)\left(x\right)=(g\circ f)\left(x\right) ($for $x\ne 0)$ is

If ${}^{\text{'}}f^{\text{'}}$ is the greatest integers function defined on $R$ as $f\left(x\right)=\left[x\right]$ and ${}^{\text{'}}g^{\text{'}}$ is the modulus function defined on $R$ as $g\left(x\right)=\left|x\right|$, then the value of $\left(gof\right)\left(\frac{-5}{3}\right)$ is

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

If $f:R\to R$ and $g:R\to R$ are two functions defined by $f\left(x\right)=ax+b\left(a\ne 0\right)\forall x\in R$ and $g\left(x\right)=c{x}^3+d\left(c\ne 0\right)\forall x\in R$, then ${\left(fog\right)}^{-1}\left(x\right)=$