MATH SOLVE

3 months ago

Q:
# I need help finding both a and b

Accepted Solution

A:

Answer:a) [tex] h^{-1}(x) = 2x + 8 [/tex]b) [tex] k^{-1}(x) = \pm\sqrt{x - 3} [/tex]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. [tex] h(x) = \dfrac{1}{2}x - 4 [/tex]Step 2. [tex] y = \dfrac{1}{2}x - 4 [/tex]Step 3. [tex] x = \dfrac{1}{2}y - 4 [/tex]Step 4. [tex] x = \dfrac{1}{2}y - 4 [/tex][tex] x + 4 = \dfrac{1}{2}y [/tex][tex] 2x + 8 = y [/tex][tex] y = 2x + 8 [/tex]Step 5. [tex] h^{-1}(x) = 2x + 8 [/tex]Now let's do part b) following the steps above.Step 1. [tex] k(x) = x^2 + 3 [/tex]Step 2. [tex] y = x^2 + 3 [/tex]Step 3. [tex] x = y^2 + 3 [/tex]Step 4. [tex] x = y^2 + 3 [/tex][tex] x - 3 = y^2 [/tex][tex] y^2 = x - 3 [/tex][tex] y = \pm\sqrt{x - 3} [/tex]Step 5. [tex] k^{-1}(x) = \pm\sqrt{x - 3} [/tex]