Find the inverse function of $f ( t ) = t ^ { 7 } - 5$ .
A) $f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t - 5 }$
B) $f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t } - 5$
C) $f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t + 5 }$
D) $f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t } + 5$
E)The function does not have an inverse.

Question

Quizplus · Accepted Answer

To find the inverse function of $f(t)$, we need to solve the equation $f(x)=t$ for $x$. So we have 
\begin{align*}
f(x)&=t\
x^7-5&=t\
x^7&=t+5\
x&=\sqrt[7]{t+5}.
\end{align*}
Thus, the inverse function is $f^{-1}(t)=\sqrt[7]{t+5}$. Option (C) matches our answer, so it is the correct choice.

Find the Inverse Function Of f(t)=t7−5f ( t ) = t ^ { 7 } - 5f(t)=t7−5

Find the Inverse Function Of $f ( t ) = t ^ { 7 } - 5$