Question

What is the inverse of the function f(x) = 2x – 10?

h(x) = 2x – 5
h(x) = 2x + 5
h(x) = one-halfx – 5
h(x) = one-halfx + 5

Answer 1

To find the inverse of the function \( f(x) = 2x - 10 \), we need to follow a few steps:

1. Replace \( f(x) \) with \( y \):
\[
y = 2x - 10
\]

2. Switch \( x \) and \( y \):
\[
x = 2y - 10
\]

3. Solve for \( y \) to get the inverse function. First, isolate \( y \):
\[
x + 10 = 2y
\]
\[
y = \frac{x + 10}{2}
\]

4. Rewrite \( y \) as \( f^{-1}(x) \):
\[
f^{-1}(x) = \frac{x + 10}{2}
\]

This can also be written as:
\[
f^{-1}(x) = \frac{1}{2}x + 5
\]

Therefore, the inverse function is:
\[
h(x) = \frac{1}{2}x + 5
\]

So, the correct option is:
\[
h(x) = \frac{1}{2}x + 5
\]

In the provided choices, it would correspond to:

h(x) = one-halfx + 5