Question

find the inverse of the function $f(x) = 2x - 4$. \
$\boldsymbol{g(x) = \frac{1}{2}x - \frac{1}{4}}$ \
$g(x) = \frac{1}{4}x - \frac{1}{2}$ \
$g(x) = 4x + 2$ \
$g(x) = \frac{1}{2}x + 2$ \
retry

Explanation:

Step1: Replace \( f(x) \) with \( y \)

\( y = 2x - 4 \)

Step2: Swap \( x \) and \( y \)

\( x = 2y - 4 \)

Step3: Solve for \( y \)

Add 4 to both sides: \( x + 4 = 2y \)
Divide both sides by 2: \( y = \frac{1}{2}x + 2 \)
So the inverse function \( g(x)=\frac{1}{2}x + 2 \)

Answer:

\( g(x)=\frac{1}{2}x + 2 \) (the option with this function, i.e., the last option: \( g(x)=\frac{1}{2}x + 2 \))