R D Sharma Solutions for Chapter: Function, Exercise 1: EXERCISE

Find $fog$ and $gof$ if $f\left(x\right)=x^2,g\left(x\right)=\cos x$.

Find $fog$ and $gof$ if $f\left(x\right)=\left|x\right|, g\left(x\right)=\sin x$.

Find $fog$ and $gof$ if $f\left(x\right)=x+1, g\left(x\right)=e^x$.

Find $fog$ and $gof$if : $f\left(x\right)=x^2+2, g\left(x\right)=1-\frac{1}{(1-x)}$

If $f\left(x\right)=\left|x\right|$, prove that $fof=f$.

If $f\left(x\right)=2x+5$ and $g\left(x\right)=x^2+1$ be two real functions, then find $fog$.

If $f\left(x\right)=2x+5$ and $g\left(x\right)=x^2+1$ be two real functions, then find $gof$.

Let $f, g, h$ be real functions given by $f\left(x\right)=\sin x, g\left(x\right)=2x$ and $h\left(x\right)=\cos x$. Prove that $fog=go\left(fh\right)$.