Answer:
[tex]f^{-1}(x)=\frac{x+15}{3}[/tex]
or
[tex]f^{-1}(x)=\frac{x}{3}+5[/tex]
Step-by-step explanation:
That means we want to find the inverse function of f(x)=3x-15.
The inverse function is just the swapping of x and y really. We tend to remake the y the subject afterwards.
So we are given:
y=3x-15
First step: Swap x and y
x=3y-15
Now it's time to solve for y.
Second step: Add 15 on both sides:
x+15=3y
Third step: Divide both sides by 3:
(x+15)/3=y
The inverse function is:
[tex]f^{-1}(x)=\frac{x+15}{3}[/tex]
You can also split up the fraction like so:
[tex]f^{-1}(x)=\frac{x}{3}+\frac{15}{3}[/tex]
The last fraction there can be reduced:
[tex]f^{-1}(x)=\frac{x}{3}+5[/tex]
