The inverse of the function f(x) is [tex]f^{-1}(x)[/tex] = 4 x + 48
Step-by-step explanation:
The steps of finding the Inverse of a function f(x)
∵ f(x) = [tex]\frac{1}{4}[/tex] x - 12
∵ f(x) = y
∴ y = [tex]\frac{1}{4}[/tex] x - 12
- Replace x by y and y by x
∴ x = [tex]\frac{1}{4}[/tex] y - 12
- Add 12 to both sides
∴ x + 12 = [tex]\frac{1}{4}[/tex] y
- Multiply each term by 4
∴ x(4) + 12(4) = [tex]\frac{1}{4}[/tex] (4) y
∴ 4 x + 48 = y
∴ y = 4 x + 48
- Replace y by [tex]f^{-1}(x)[/tex]
∴ [tex]f^{-1}(x)[/tex] = 4 x + 48
The inverse of the function f(x) is [tex]f^{-1}(x)[/tex] = 4 x + 48
Learn more:
You can learn more about the inverse of the functions in brainly.com/question/628130
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