Question

If $f\left(x\right)=x+7$ and $g\left(x\right)=x-7$, $x\in R$, find $\left(fog\right)\left(7\right)$. function $f:R\to R$ defined by $f\left(x\right)=\frac{3x+5}{2}$ is an invertible function, find $f^{-1}$

Answer 1

$f\left(x\right)=x+7$

$g\left(x\right)=x-7,x\in R$

$fog\left(x\right)=f(x-7)\left(x\right)$

$=(x-7+7)\left(x\right)$

$=x$

$fog\left(7\right)=7$

$f\left(x\right)=\frac{3x+5}{2}$

$y=\frac{3x+5}{2}$

Swapping

$x=\frac{3y+5}{2}$

$2x=3y+5$

$2x-5=3y$

$y=\frac{2x-5}{3}$

$f^{-1}\left(x\right)=\frac{2x-5}{3}$