Question

Find the inverse function of the function f, of, x, equals, one fifth, x, plus, 3f(x)=
5
1
​
x+3

Answer 1

To find the inverse function of \( f(x) = \frac{1}{5}x + 3 \), we can follow these steps:

1. **Replace \( f(x) \) with \( y \)**:
\[
y = \frac{1}{5}x + 3
\]

2. **Swap \( x \) and \( y \)**:
\[
x = \frac{1}{5}y + 3
\]

3. **Solve for \( y \)**:
- First, subtract 3 from both sides:
\[
x - 3 = \frac{1}{5}y
\]
- Next, multiply both sides by 5:
\[
5(x - 3) = y
\]
- Simplify:
\[
y = 5x - 15
\]

4. **Write the inverse function**:
The inverse function is:
\[
f^{-1}(x) = 5x - 15
\]

Thus, the inverse function \( f^{-1}(x) \) is \( 5x - 15 \).