Find the inverse of the function f(x) = 5x/4

Question

.(1 point)
Responses

f−1(x) = 5x/4

f−1(x) = 4x5
f−1(x) = 4x/5

f−1(x) = 4/5x

f−1(x) = 5/4x

Answer 1

To find the inverse of the function \( f(x) = \frac{5x}{4} \), we can follow these steps:

1. Start by replacing \( f(x) \) with \( y \): \[ y = \frac{5x}{4} \]

2. Swap \( x \) and \( y \): \[ x = \frac{5y}{4} \]

3. Solve for \( y \): \[ 4x = 5y \] \[ y = \frac{4x}{5} \]

4. This gives us the inverse function: \[ f^{-1}(x) = \frac{4x}{5} \]

Thus, the correct response is \( f^{-1}(x) = \frac{4x}{5} \).