Question

I need help finding both a and b

Answer 1

a)

`h^(-1)(x) = 2x + 8`

b)

`k^(-1)(x) = \pm√(x - 3)`

Explanation:

To find an inverse function, follow these steps.

Step 1. Write the function.

Step 2. Replace the function name in function notation with y.

Step 3. Switch x and y.

Step 4. Solve for y.

Step 5. Replace y with function notation for inverse function.

Now let's do part a) following the steps above.

Step 1.

`h(x) = (1)/(2)x - 4`

Step 2.

`y = (1)/(2)x - 4`

Step 3.

`x = (1)/(2)y - 4`

Step 4.

`x = (1)/(2)y - 4`

`x + 4 = (1)/(2)y`

`2x + 8 = y`

`y = 2x + 8`

Step 5.

`h^(-1)(x) = 2x + 8`

Now let's do part b) following the steps above.

Step 1.

`k(x) = x^2 + 3`

Step 2.

`y = x^2 + 3`

Step 3.

`x = y^2 + 3`

Step 4.

`x = y^2 + 3`

`x - 3 = y^2`

`y^2 = x - 3`

`y = \pm√(x - 3)`

Step 5.

`k^(-1)(x) = \pm√(x - 3)`