Question

Find the inverse of h(x)=16x−5 algebraically.
A. h
−1
(x)=16x+5
B. h
−1
(x)=
16
x
​
+5
C. h
−1
(x)=
16
x−5
​

D. h
−1
(x)=
16
x+5
​

Answer 1

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

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

2. **Solve for \( x \) in terms of \( y \):**
\[
y + 5 = 16x
\]
\[
x = \frac{y + 5}{16}
\]

3. **Interchange \( x \) and \( y \) to find the inverse:**
\[
h^{-1}(x) = \frac{x + 5}{16}
\]

Now, let's compare this with the answer choices provided.

The inverse function is:
\[
h^{-1}(x) = \frac{x + 5}{16}
\]

After examining answer choices:
- A. \( h^{-1}(x) = 16x + 5 \)
- B. \( h^{-1}(x) = \frac{16}{x} + 5 \)
- C. \( h^{-1}(x) = 16x - 5 \)
- D. \( h^{-1}(x) = 16x + 5 \)

It appears that none of the answer choices provided match \( h^{-1}(x) = \frac{x + 5}{16} \).

Please check if there was a mistake in the provided answer options or in interpreting the function. The correct inverse is \( h^{-1}(x) = \frac{x + 5}{16} \).