Find the inverse of h(x)=16x−5

Question

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