Question

Find the inverse function of f(x)=x-10/2.

Answer 1

To find the inverse function of \( f(x) = \frac{x - 10}{2} \), we will follow these steps:

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

2. Swap \( x \) and \( y \):
\[
x = \frac{y - 10}{2}
\]

3. Solve for \( y \):
First, multiply both sides by 2 to get rid of the denominator:
\[
2x = y - 10
\]

Next, add 10 to both sides:
\[
y = 2x + 10
\]

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

Thus, the inverse function is:
\[
f^{-1}(x) = 2x + 10
\]