Question

I would appreciate it if I could get a step-by-step on how to solve this problem. Thank you.!

Answer 1

Answers: -2, $\frac{x+4}{3}$, -1

Explanation:

Inverse is when the x's and y's are swapped.

g(x) = (-4, 8), (-2, 9), (4, 7), (9, -1)

g⁻¹(x) = (8, -4), (9, -2), (7, 4), (-1, 9)

g⁻¹(9) = ??? when x = 9, what is y?  Answer: -2

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h(x) = 3x - 4

To find the inverse, let y represent h(x).  Then swap the x's and y's and solve for y:

x  = 3y - 4

+4       +4

x + 4 = 3y

$\frac{x+4}{3}$ = y

h⁻¹(x) = $\frac{x+4}{3}$

*******************************************************************

h(-1) = 3(-1) - 4

       =  -3  - 4

       = -7

h⁻¹(h(-1)) = h⁻¹(-7)

h⁻¹(-7) = $\frac{-7+4}{3}$  

        = $\frac{-3}{3}$  

        = -1