Question

For the function f(x)=8x−9
, find f−1(x)
.(1 point)
Responses

f−1(x)=(x−9)8
f inverse of x is equal to the fraction with numerator open paren x minus 9 close paren and denominator 8

f−1(x)=x8+9
f inverse of x is equal to x over 8 plus 9

f−1(x)=8x+9
f inverse of x is equal to 8 x plus 9

f−1(x)=(x+9)8
f inverse of x is equal to the fraction with numerator open paren x plus 9 close paren and denominator 8

Answer 1

To find the inverse of the function \( f(x) = 8x - 9 \), we follow these steps:

1. **Replace \( f(x) \) with \( y \)**:
\[
y = 8x - 9
\]

2. **Swap \( x \) and \( y \)**:
\[
x = 8y - 9
\]

3. **Solve for \( y \)**:
\[
x + 9 = 8y
\]
\[
y = \frac{x + 9}{8}
\]

So, the inverse function is:
\[
f^{-1}(x) = \frac{x + 9}{8}
\]

Now, let's match it with the given responses:

The correct option is:
- **f−1(x) is equal to the fraction with numerator (x + 9) and denominator 8.**