Answer:
[tex]g(x) = \frac{1}{4} x - 3[/tex]
Step-by-step explanation:
Since g(x) is the inverse of f (x) to find g(x) must first find f-¹(x)
To find f-¹(x) equate f(x) to y
That's
f(x) = y
y = 4x + 12
Next interchange the terms x becomes y and y becomes x
That's
x = 4y + 12
Next make y the subject
4y = x - 12
Divide both sides by 4
[tex]y = \frac{1}{4} x - 3[/tex]
Therefore
[tex]g(x) = \frac{1}{4} x - 3[/tex]
Hope this helps you
