Answer:
The inverse of h(x) is [tex]\frac{5x-6}{2}[/tex]
Step-by-step explanation:
* Lets explain how to make the inverse of a function
- To find the inverse of a function we switch x and y and then solve
for new y
- You can make it with these steps
# write g(x) = y
# switch x and y
# solve for y
# write y as [tex]g^{-1}(x)[/tex]
* Lets solve the problem
∵ [tex]h(x)=\frac{2x+6}{5}[/tex]
# Step 1
∴ [tex]y=\frac{2x+6}{5}[/tex]
# Step 2
∴ [tex]x=\frac{2y+6}{5}[/tex]
# Step 3
∵ [tex]x=\frac{2y+6}{5}[/tex]
- Multiply each side by 5
∴ 5x = 2y + 6
- Subtract 6 from both sides
∴ 5x - 6 = 2y
- Divide both sides by 2
∴ [tex]y=\frac{5x-6}{2}[/tex]
# Step 4
∴ [tex]h^{-1}(x)=\frac{5x-6}{2}[/tex]
