Question

10. Find the inverse of the function f(x) = 36x7, x ≤ 0.

Answer 1

`\boxed{f^(-1)(x)=\sqrt[7]{(y)/(36)}}`

Explanation:

The inverse of the function satisfies the following:

`f(a)=b \qquad \Rightarrow \qquad f^(-1)(b)=a`

Given the expression:

`f(x)=36x^7`

The inverse function can be calculated with the next steps:

• replace
  `f(x)` con
  `y`
• Solve for the variable x based on the variable y.
• Variables are swapped.

`\begin{aligned}f(x)=36x^7 & \rightarrow y=36x^7 \\ &= (y)/(36)=x^7 \\ &= \sqrt[7]{(y)/(36)}=x \\& \therefore f^(-1)(x)= \sqrt[7]{(y)/(36)}\end{aligned}`

`\text{-B$\mathfrak{randon}$VN}`