Question

Find gof and fog, if
(i) f(x) =|x| and g(x) =|5x-2|

$\left(ii\right)f\left(x\right)=8x^3$ and $g\left(x\right)=x^{\frac{1}{3}}$.

Answer 1

(i) f(x)=|x|and g(x)=|5x-2|
$\therefore$ (gof)(x)=g(f(x))=g(|x|)=|5|x|-2|
and fog(x)=f(g(x)) = f(|5x-2|)=||5x-2||=|5x-2|

(ii) $f\left(x\right)=8x^3$ and $g\left(x\right)=x^{\frac{1}{3}}$
$\therefore \left(gof\right)\left(x\right)=g\left(f\right(x\left)\right)=g\left(8x^3\right)=(8x^3{)}^{\frac{1}{3}}=2x$
and $fog\left(x\right)=f\left(g\right(x\left)\right)=f\left(x^{\frac{1}{3}}\right)=8(x^{\frac{1}{3}}{)}^3=8x$.