Question

Find the inverse of the function y=3x−4−−−−√
𝑦
=
3
𝑥
−
4
.(1 point)
Responses

f−1(x)=x29−4
𝑓
−
1
(
𝑥
)
=
𝑥
2
9
−
4
f inverse left parenthesis x right parenthesis equals Start Fraction x squared over 9 End Fraction minus 4

f−1(x)=x29+4
𝑓
−
1
(
𝑥
)
=
𝑥
2
9
+
4
f inverse left parenthesis x right parenthesis equals Start Fraction x squared over 9 End Fraction plus 4

f−1(x)=x23+4
𝑓
−
1
(
𝑥
)
=
𝑥
2
3
+
4
f inverse left parenthesis x right parenthesis equals Start Fraction x squared over 3 End Fraction plus 4

f−1(x)=x23−4

Answer 1

To find the inverse of the function \( y = \sqrt{3x - 4} \), we need to follow these steps:

1. **Rewrite the equation** with \( y \) on one side:
\[
y = \sqrt{3x - 4}
\]

2. **Square both sides** to eliminate the square root:
\[
y^2 = 3x - 4
\]

3. **Solve for \( x \)**:
\[
3x = y^2 + 4
\]
\[
x = \frac{y^2 + 4}{3}
\]

4. **Switch \( x \) and \( y \)** to find the inverse:
\[
y = \frac{x^2 + 4}{3}
\]

Thus, the inverse function is:
\[
f^{-1}(x) = \frac{x^2 + 4}{3}
\]

By comparing this with your options, the correct answer corresponds to:
\[
f^{-1}(x) = \frac{x^2}{3} + 4
\]

So, the correct statement would be:
\[
f^{-1}(x) = \frac{x^2}{3} + 4
\]

Make sure to check what is given in your alternatives and select this one.