Find the inverse function of the function f, of, x, equals, 2, x, plus, 9f(x)=2x+9.

Question

Answer
Attempt 1 out of 2
Multiple Choice Answers
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, x, minus, 9, divided by, 2, end fractionf
−1
(x)=
2
x−9
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, x, minus, 2, divided by, 9, end fractionf
−1
(x)=
9
x−2
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, x, plus, 2, divided by, 9, end fractionf
−1
(x)=
9
x+2
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, x, plus, 9, divided by, 2, end fractionf
−1
(x)=
2
x+9
​

Answer 1

To find the inverse function of \( f(x) = 2x + 9 \), we will follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = 2x + 9 \]

2. Swap \( x \) and \( y \): \[ x = 2y + 9 \]

3. Solve for \( y \): \[ x - 9 = 2y \] \[ y = \frac{x - 9}{2} \]

4. Write down the inverse function: \[ f^{-1}(x) = \frac{x - 9}{2} \]

Now we can compare this result with the provided multiple choice answers:

1. \( f^{-1}(x) = \frac{x - 9}{2} \)
2. \( f^{-1}(x) = \frac{x - 2}{9} \)
3. \( f^{-1}(x) = \frac{x + 2}{9} \)
4. \( f^{-1}(x) = \frac{x + 9}{2} \)

The correct inverse function is: \[ f^{-1}(x) = \frac{x - 9}{2} \]

Thus, the answer is the first option: \[ f^{-1}(x) = \frac{x - 9}{2} \]