Question:
If g(x) is the inverse of f(x) and f(x) = 4x+12 what is g(x)?
Answer:
[tex]g(x) = \frac{x}{4} -3[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 4x + 12[/tex]
Required
Find g(x)
[tex]f(x) = 4x + 12[/tex]
Replace f(x) with y
[tex]y = 4x + 12[/tex]
Swap the positions of y and x
[tex]x = 4y + 12[/tex]
Make y the subject: Subtract 12 from both sides
[tex]x -12= 4y + 12-12[/tex]
[tex]x -12= 4y[/tex]
Make y the subject: Divide through by 3
[tex]\frac{x}{4} -\frac{12}{4}= \frac{4y }{4}[/tex]
[tex]\frac{x}{4} -\frac{12}{4}= y[/tex]
[tex]y = \frac{x}{4} -\frac{12}{4}[/tex]
Since g(x) is the inverse, replace y with g(x)
[tex]g(x) = \frac{x}{4} -\frac{12}{4}[/tex]
[tex]g(x) = \frac{x}{4} -3[/tex]
