Question

Given that the function $h(x)=x^3+2x+1$ for $x\in R$ has an inverse $h^{-1}$ on $R$, then the value of ${\left(h^{-1}\right)}^{\prime }(1)$ is

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. 3
• D. 2

Answer 1

Answer: (B)

$\therefore {\left(h^{-1}\right)}^{\prime }=(1)=\frac{1}{h^{\prime }(0)}=\frac{1}{2}$
$\text{ As }h(x)=x^3+2x+1$
$\Rightarrow h^{\prime }(x)=3x^2+2$