Answer:
a. [tex]f^-^1(x)=\frac{x}{4} +3[/tex]
b. [tex]f(-9)=-48[/tex]
c. [tex]f^-^1(-9)=\frac{3}{4}[/tex]
Step-by-step explanation:
In a, the -1 means inverse of f(x). To find the inverse, you rewrite the equation in terms of x and y. You replace the x with y and y with x. Then you solve for y.
[tex]f^-^1(x)=4x-12[/tex]
[tex]y=4x-12[/tex]
[tex]x=4y-12[/tex]
[tex]x+12=4y[/tex]
[tex]\frac{x}{4} +3=y[/tex]
[tex]f^-^1(x)=\frac{x}{4} +3[/tex]
In b, all you have to do is plug in -9 into f(x).
[tex]f(9)=4(9)-12[/tex]
[tex]f(9)=-48[/tex]
In c, you plug in -9 into inverse function f.
[tex]f^-^1(-9)=\frac{3}{4}[/tex]
