Question

dentify the inverse to the function f(x)=3x/4+1/2
.(1 point)
Responses

f^−1(x)=4x/3−1/2
f inverse of x is equal to 4 x over 3 minus 1 half

f^−1(x)=4x−2/3
f inverse of x is equal to the fraction with numerator 4 x minus 2 and denominator 3

f/−1(x)=3x/4−1/2
f inverse of x is equal to 3 x over 4 minus 1 half

Answer 1

To find the inverse of the function \( f(x) = \frac{3x}{4} + \frac{1}{2} \), we will follow these steps:

1. Replace \( f(x) \) with \( y \):
\[
y = \frac{3x}{4} + \frac{1}{2}
\]

2. Swap \( x \) and \( y \):
\[
x = \frac{3y}{4} + \frac{1}{2}
\]

3. Solve for \( y \):
- Subtract \( \frac{1}{2} \) from both sides:
\[
x - \frac{1}{2} = \frac{3y}{4}
\]
- Multiply both sides by 4 to eliminate the fraction:
\[
4\left(x - \frac{1}{2}\right) = 3y
\]
\[
4x - 2 = 3y
\]
- Now, divide by 3:
\[
y = \frac{4x - 2}{3}
\]

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

So, the correct response is:
**f^−1(x)=4x−2/3**
**f inverse of x is equal to the fraction with numerator 4 x minus 2 and denominator 3**