if the function (f) is defined by $f(x)=x^{5}-1$, then $f^{-1}$, the inverse function of (f), is defined by…

if the function (f) is defined by $f(x)=x^{5}-1$, then $f^{-1}$, the inverse function of (f), is defined by $f^{-1}(x)=$

if the function (f) is defined by $f(x)=x^{5}-1$, then $f^{-1}$, the inverse function of (f), is defined by $f^{-1}(x)=$

Answer

Explanation:

Step1: Let $y = f(x)$

$y=x^{5}-1$

Step2: Solve for $x$ in terms of $y$

$y + 1=x^{5}$, then $x=\sqrt[5]{y + 1}$

Step3: Replace $x$ with $f^{-1}(x)$ and $y$ with $x$

$f^{-1}(x)=\sqrt[5]{x + 1}$

Answer:

$f^{-1}(x)=\sqrt[5]{x + 1}$