Question

Find the inverse of the function algebraically. Show all of your work.

k(x) = 1/3x + 7

Answer 1

To find the inverse of the function \( k(x) = \frac{1}{3}x + 7 \), follow these steps:

1. **Replace \( k(x) \) with \( y \)**:
\[
y = \frac{1}{3}x + 7
\]

2. **Swap \( x \) and \( y \)**:
\[
x = \frac{1}{3}y + 7
\]

3. **Solve for \( y \)**:
- First, isolate the term involving \( y \):
\[
x - 7 = \frac{1}{3}y
\]
- Next, multiply both sides by 3 to eliminate the fraction:
\[
3(x - 7) = y
\]
- Distribute the 3:
\[
y = 3x - 21
\]

4. **Write the inverse function**:
The inverse function is given by:
\[
k^{-1}(x) = 3x - 21
\]

Thus, the inverse of the function \( k(x) \) is:
\[
k^{-1}(x) = 3x - 21
\]