Answer:
[tex]g(x)=\frac{1}{4}x-3[/tex]
Step-by-step explanation:
we have
[tex]f(x)=4x+12[/tex]
Find the inverse
step 1
Let
y=f(x)
[tex]y=4x+12[/tex]
step 2
Exchange the variables (x for y and y for x)
[tex]x=4y+12[/tex]
step 3
Isolate the variable y
we have
[tex]x=4y+12[/tex]
Subtract 12 both sides
[tex]x-12=4y[/tex]
Divide by 4 both sides
[tex]y=\frac{x-12}{4}[/tex]
simplify
[tex]y=\frac{1}{4}x-3[/tex]
step 4
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=\frac{1}{4}x-3[/tex]
we have that
[tex]g(x)=f^{-1}(x)[/tex]
therefore
[tex]g(x)=\frac{1}{4}x-3[/tex]
