Answer:
[tex]f(x)^{-1}[/tex] = [tex]\frac{x+9}{4}[/tex].
Step-by-step explanation:
Given : f(x)=4x-9.
To find : Which is the inverse of the function.
Solution : We have given f(x)=4x-9.
Step 1 : replace y to x
x = 4y -9.
Step 2: solve for y
On adding by 9 both side
x + 9 = 4y
On dividing by 4 both sides
y = [tex]\frac{x+9}{4}[/tex].
y = [tex]f(x)^{-1}[/tex].
Then [tex]f(x)^{-1}[/tex] = [tex]\frac{x+9}{4}[/tex].
Therefore, [tex]f(x)^{-1}[/tex] = [tex]\frac{x+9}{4}[/tex].
