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,
`(x+4)/(3)`, -1

Step-by-step 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

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

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

`(x+4)/(3)` = y

h⁻¹(x) =
`(x+4)/(3)`

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

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

= -3 - 4

= -7

h⁻¹(h(-1)) = h⁻¹(-7)

h⁻¹(-7) =
`(-7+4)/(3)`

=
`(-3)/(3)`

= -1