Question

Find the inverse of h(x)=16x−5
algebraically.(1 point)
Responses

h^−1(x)=x−5/16
h inverse left parenthesis x right parenthesis equals Start Fraction x minus 5 over 16 End Fraction

h^−1(x)=x+5/16
h inverse left parenthesis x right parenthesis equals Start Fraction x plus 5 over 16 End Fraction

h^−1(x)=16x+5
h inverse left parenthesis x right parenthesis equals 16 x plus 5

h^−1(x)=x/16+5

Answer 1

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

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

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

3. Solve for \( y \):
\[
x + 5 = 16y
\]
\[
y = \frac{x + 5}{16}
\]

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

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

The correct response from your options is:
\[
h^{-1}(x) = \frac{x + 5}{16}
\]