Question

Find the inverse of h(x)=16x−5
algebraically.

Answer 1

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

1. **Replace \( h(x) \) with \( y \)**:

\[
y = 16x - 5
\]

2. **Solve for \( x \)** in terms of \( y \)**:

First, add 5 to both sides:

\[
y + 5 = 16x
\]

Next, divide both sides by 16:

\[
x = \frac{y + 5}{16}
\]

3. **Swap \( x \) and \( y \)** to express the inverse function:

\[
y = \frac{x + 5}{16}
\]

4. **Thus, the inverse function** is:

\[
h^{-1}(x) = \frac{x + 5}{16}
\]

So the inverse of the function \( h(x) = 16x - 5 \) is \( h^{-1}(x) = \frac{x + 5}{16} \).