Answer:
[tex]f^{-1}(x)[/tex]= [tex]\frac{1}{4x-12)}[/tex].
Step-by-step explanation:
Given : f(x) = [tex]\frac{1}{4x}+3[/tex].
To find : inverse
Solution : We have given f(x) = [tex]\frac{1}{4x}+3[/tex].
Step 1: f(x) = y
y = [tex]\frac{1}{4x}+3[/tex].
Step 2: replace x and y .
x = [tex]\frac{1}{4y}+3[/tex].
Step 3:
Solve for y
On subtracting both sides by 3
x -3 = [tex]\frac{1}{4y}[/tex].
Taking reciprocal both sides
4y = [tex]\frac{1}{x-3}[/tex].
On dividing both sides by 4
y = [tex]\frac{1}{4(x-3)}[/tex].
Take [tex]f^{-1}(x)=y[/tex].
[tex]f^{-1}(x)[/tex]= [tex]\frac{1}{4(x-3)}[/tex].
Therefore, [tex]f^{-1}(x)[/tex]=[tex]\frac{1}{4x-12}[/tex].
