Question

I need help finding both a and b

Answer 1

Answer:

a)

$h^{-1}(x) = 2x + 8$

b)

$k^{-1}(x) = \pm\sqrt{x - 3}$

Step-by-step 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.

$h(x) = \dfrac{1}{2}x - 4$

Step 2.

$y = \dfrac{1}{2}x - 4$

Step 3.

$x = \dfrac{1}{2}y - 4$

Step 4.

$x = \dfrac{1}{2}y - 4$

$x + 4 = \dfrac{1}{2}y$

$2x + 8 = y$

$y = 2x + 8$

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.

$x = y^2 + 3$

$x - 3 = y^2$

$y^2 = x - 3$

$y = \pm\sqrt{x - 3}$

Step 5.

$k^{-1}(x) = \pm\sqrt{x - 3}$