Find the inverse of the function f(x) = 5x4

Question

.(1 point)
Responses

f−1(x) = 5x4
f−1(x) = 5x4

f−1(x) = 4x5
f−1(x) = 4x5

f−1(x) = 45x
f−1(x) = 45x

f−1(x) = 54x
f−1(x) = 54x

Answer 1

To find the inverse of the function \( f(x) = 5x^4 \), we need to follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = 5x^4 \]

2. Swap \( x \) and \( y \): \[ x = 5y^4 \]

3. Solve for \( y \): \[ y^4 = \frac{x}{5} \] \[ y = \left( \frac{x}{5} \right)^{1/4} \]

4. Therefore, the inverse function is: \[ f^{-1}(x) = \left( \frac{x}{5} \right)^{1/4} \]

None of the provided responses accurately reflect this inverse function.

If you need further assistance or clarification about finding inverses or other functions, feel free to ask!