Question

If f(x)=5x+4, what is the inverse of f(x)?

Answer 1

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

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

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

3. Solve for \( y \):
- First, isolate the term with \( y \):
\[
x - 4 = 5y
\]
- Then, divide by 5:
\[
y = \frac{x - 4}{5}
\]

4. Now, write the inverse function, which is denoted as \( f^{-1}(x) \):
\[
f^{-1}(x) = \frac{x - 4}{5}
\]

So, the inverse of \( f(x) = 5x + 4 \) is:
\[
f^{-1}(x) = \frac{x - 4}{5}
\]