Question

Let $f:R\to R,g:R\to R$ be two function given by $f\left(x\right)=2x-3,g\left(x\right)=x^3+5$. Then $\left(fog{)}^{-1}\right\{x\}$ is equal to

• A. ${\left(\frac{x+7}{2}\right)}^{1/3}$
• B. ${(x-\frac{7}{2})}^{1/3}$
• C. ${\left(\frac{x-2}{7}\right)}^{1/3}$
• D. ${\left(\frac{x-7}{2}\right)}^{1/3}$

Answer 1

The correct option is D ${\left(\frac{x-7}{2}\right)}^{1/3}$

$f\left(g\right(x\left)\right)$
$=f(x^3+5)$
$=2(x^3+5)-3$
$=2x^3+7$
$h\left(x\right)=2x^3+7$
$y=2x^3+7$
${\left(\frac{y-7}{2}\right)}^{\frac{1}{3}}=x$
Hence inverse is ${\left(\frac{x-7}{2}\right)}^{\frac{1}{3}}$