To find the inverse function of [tex]\( f(x) = 2x - 4 \)[/tex], we follow these steps:
1. Write down the function:
[tex]\[
y = 2x - 4
\][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse:
[tex]\[
x = 2y - 4
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[
x + 4 = 2y
\][/tex]
[tex]\[
y = \frac{x + 4}{2}
\][/tex]
4. Express the result in the form [tex]\( f^{-1}(x) = ax + b \)[/tex]:
[tex]\[
f^{-1}(x) = \frac{1}{2}x + 2
\][/tex]
Therefore, the completed inverse function is:
[tex]\[
f^{-1}(x) = 0.5x + 2
\][/tex]
So, in the blanks:
[tex]\[
f^{-1}(x) = \boxed{0.5} x + \boxed{2}
\][/tex]
