Question

find the inverse of h(x)=16x-5 algebraically

Answer 1

To find the inverse of the function \( h(x) = 16x - 5 \), we follow these steps:

1. **Replace \( h(x) \) with \( y \)**:
\[
y = 16x - 5
\]

2. **Swap \( x \) and \( y \)**:
\[
x = 16y - 5
\]

3. **Solve for \( y \)**:
- Add 5 to both sides:
\[
x + 5 = 16y
\]
- Divide both sides by 16:
\[
y = \frac{x + 5}{16}
\]

4. **Replace \( y \) with \( h^{-1}(x) \)**:
\[
h^{-1}(x) = \frac{x + 5}{16}
\]

Thus, the inverse of \( h(x) = 16x - 5 \) is:
\[
h^{-1}(x) = \frac{x + 5}{16}
\]