Embibe Experts Solutions for Chapter: Functions, Exercise 1: TS EAMCET - 5 August 2021 Shift 1

$A$ and $B$ are subsets of $R.$ Every element $x$ of $A$ is mapped to an element of $B$ by the rule, $y\left(x\right)=\left\{\begin{array}{cc}\frac{5x}{\left(x-3\right)\left(x+3\right)}& \mathrm{if} x\ne -1\\ -1& \mathrm{if} x=-1\end{array}\right.,$ then $A=$

The domain and range of $y\left(x\right)=\cos x-3$ are respectively

Let $f\left(x\right)=\frac{1}{2}-\tan \left(\frac{\pi x}{2}\right), -1<x<1$ and $g\left(x\right)=\sqrt{3+4x-4x^2}$, then the domain of $\left(f+g\right)$ is

Let $a>1$ be a constant. If $f:A\to A$ and $\left(x, y\right)\in f$ satisfy $a^x+a^y=a,$ then $A=$

If $f:\mathrm{ℝ}\to \mathrm{ℝ}$ is defined as $f\left(x\right)=\frac{3^x+3^{-x}}{2}, \forall x\in \mathrm{ℝ}$ and it satisfies $f(x+y)+f(x-y)=af\left(x\right)f\left(y\right),$ then $a=$

If $f\left(1\right)=0$ and $f(n+1)-f\left(n\right)=5n\forall n\in N$ then $f\left(n\right)=$

For $x\in R-\{-6\},$ the value of $\frac{(x+2)(x+5)}{(x+6)}$ does not lie in the interval

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