Mathematics

Question

if f(x)=1/2 x-6 what is the equation for f–1(x)?

A. f–1(x) = 2x + 6

B. f–1(x) = 2x – 6

C. f–1(x) = 2(x + 6)

D. f–1(x) = 2(x – 6)

2 Answer

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  • Answer:

    Option C [tex]f^{-1}(x)=2(x+6)[/tex]

    Step-by-step explanation:

    we have that

    [tex]f(x)=\frac{1}{2}x-6[/tex]

    Let

    [tex]y=f(x)[/tex]

    [tex]y=\frac{1}{2}x-6[/tex]

    Exchange the variables x for y and y for x

    [tex]x=\frac{1}{2}y-6[/tex]

    Isolate the variable y

    [tex]x+6=\frac{1}{2}y[/tex]

    [tex]y=2(x+6)[/tex]

    Let

    [tex]f^{-1}(x)=y[/tex]

    [tex]f^{-1}(x)=2(x+6)[/tex]

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