[tex]g(x)=\frac{x}{4}-3[/tex] if g(x) is the inverse of f(x) = 4x+12.
Step-by-step explanation:
Given that,
f(x) = 4x + 12
To find g(x) Let f(x) = y
y = 4x+12
Subtract 12 from both side
y -12 = 4x + 12 - 12
y – 12 = 4x
Solve to find x
[tex]x=\frac{y}{4}-\frac{12}{4}[/tex]
[tex]x=\frac{y}{4}-3[/tex]
We know that from f(x) = y
[tex]x=f^{-1}(y)[/tex]
[tex]f^{-1}(y)=\frac{y}{4}-3[/tex]
From the question we know that g(x) is the inverse of f(x)
Thus [tex]g(x)=\frac{x}{4}-3[/tex] when g(x) is the inverse of f(x)=4x+12.
