Answer:
h(x) = 3x -6.
Step-by-step explanation:
Given :f(x) = [tex]\frac{1x}{3} + 2[/tex].
To find : inverse .
Solution : We have given that
f(x) = [tex]\frac{1x}{3} + 2[/tex].
Step 1) y = [tex]\frac{1x}{3} + 2[/tex].
Step 2) Now, interchange x and y.
x = [tex]\frac{y}{3} + 2[/tex].
Step 3:
Solve for y
On subtracting both sides by 2
x -2 = [tex]\frac{y}{3}[/tex].
On multiplying both the sides by 3
3 ( x -2) = y
On taking reciprocal
y = 3x -6
This the inverse of f(x) = h(x)
Therefore, h(x) = 3x -6.
