Question

Find the inverse function of the function f, of, x, equals, 3, x, plus, 7f(x)=3x+7.
Answer
Multiple Choice Answers
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, one third, x, minus, 7f
−1
(x)=
3
1
​
x−7
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, x, plus, 7, divided by, 3, end fractionf
−1
(x)=
3
x+7
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, x, minus, 7, divided by, 3, end fractionf
−1
(x)=
3
x−7
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 3, x, minus, 7f
−1
(x)=3x−7

Answer 1

To find the inverse function \( f^{-1}(x) \) of the given function \( f(x) = 3x + 7 \), follow these steps:

1. **Replace \( f(x) \) with \( y \)**:
\[
y = 3x + 7
\]

2. **Swap \( x \) and \( y \)**:
\[
x = 3y + 7
\]

3. **Solve for \( y \)**:
- First, isolate \( 3y \) by subtracting 7 from both sides:
\[
x - 7 = 3y
\]
- Then, divide both sides by 3:
\[
y = \frac{x - 7}{3}
\]

4. **Write the inverse function**:
\[
f^{-1}(x) = \frac{x - 7}{3}
\]

Now, let's match it to the provided answer choices:

The correct answer is:
\[
f^{-1}(x) = \frac{x - 7}{3}
\]

So, the correct multiple choice answer is:
- **f, to the power minus 1, left parenthesis, x, right parenthesis, equals, start fraction, x, minus, 7, divided by, 3, end fraction**.