Answer:
[tex]g(x)=\frac{x}{4} -3[/tex]
Step-by-step explanation:
Ve have the function:
[tex]f(x)=y=4x+12[/tex]
The first step to find the inverse is to exchange the variables, that is where we see [tex]x[/tex] put [tex]y[/tex] and where we see [tex]y[/tex] put [tex]x[/tex]:
[tex]x=4y+12[/tex]
And we clear for the variable [tex]y[/tex]:
[tex]x-12=4y\\\frac{x-12}{4} =y\\\frac{x}{4} -3=y[/tex]
This would be the inverse of the function (since we know that [tex]y=f(x)[/tex]), and according to the problem the inverse of [tex]f(x)[/tex] is [tex]g(x)[/tex], so:
[tex]g(x)=\frac{x}{4} -3[/tex]
