Question

Find the inverse of the function f(x) = 5x/4
.(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 \( f^{-1}(x) = \frac{4x}{5} \).