Question

Find the inverse of h(x) = alt="\frac{2x+6}{5}" align="absmiddle" class="latex-formula">

show work please!

Answer 1

Answer:

The inverse of h(x) is $\frac{5x-6}{2}$

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 $g^{-1}(x)$

* Lets solve the problem

∵ $h(x)=\frac{2x+6}{5}$

# Step 1

∴ $y=\frac{2x+6}{5}$

# Step 2

∴ $x=\frac{2y+6}{5}$

# Step 3

∵ $x=\frac{2y+6}{5}$

- Multiply each side by 5

∴ 5x = 2y + 6

- Subtract 6 from both sides

∴ 5x - 6 = 2y

- Divide both sides by 2

∴ $y=\frac{5x-6}{2}$

# Step 4

∴ $h^{-1}(x)=\frac{5x-6}{2}$