Question

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

Answer 1

To find the inverse function of \( f(x) = \frac{x - 10}{2} \), let's follow the steps to find the inverse:

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

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

3. **Solve for \( y \)**:
- Multiply both sides by 2:
\[
2x = y - 10
\]
- Add 10 to both sides:
\[
y = 2x + 10
\]

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

Now, we need to evaluate \( f^{-1}(2) \):
\[
f^{-1}(2) = 2(2) + 10 = 4 + 10 = 14
\]

Thus, \( f^{-1}(2) = 14 \).