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Complete the inverse function for the function given below.

[tex]
\begin{array}{c}
f(x) = 2x - 4 \\
f^{-1}(x) = \square x + \square \\
\end{array}
\]

Sagot :

GinnyAnswer
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]
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