Question

Find the inverse function of the function f, of, x, equals, one fifth, x, plus, 5f(x)=
5
1
​
x+5.
Answer
Attempt 1 out of 2
Multiple Choice Answers
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 5, x, minus, 5f
−1
(x)=5x−5
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 5, x, minus, 25f
−1
(x)=5x−25
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, one fifth, x, minus, 25f
−1
(x)=
5
1
​
x−25
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, one fifth, x, minus, 5f
−1
(x)=
5
1
​
x−5

Answer 1

To find the inverse function of \( f(x) = \frac{1}{5}x + 5 \), we will follow these steps:

1. **Replace \( f(x) \) with \( y \)**:
\[
y = \frac{1}{5}x + 5
\]

2. **Swap \( x \) and \( y \)**:
\[
x = \frac{1}{5}y + 5
\]

3. **Solve for \( y \)**:
- First, isolate the term with \( y \).
\[
x - 5 = \frac{1}{5}y
\]
- Now, multiply both sides by 5 to get rid of the fraction:
\[
5(x - 5) = y
\]
- Simplify:
\[
y = 5x - 25
\]

4. **Write the inverse function**:
\[
f^{-1}(x) = 5x - 25
\]

Thus, the correct answer from the provided options is:
\[
f^{-1}(x) = 5x - 25
\]