Answers: -2, [tex]\frac{x+4}{3}[/tex], -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
[tex]\frac{x+4}{3}[/tex] = y
h⁻¹(x) = [tex]\frac{x+4}{3}[/tex]
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h(-1) = 3(-1) - 4
= -3 - 4
= -7
h⁻¹(h(-1)) = h⁻¹(-7)
h⁻¹(-7) = [tex]\frac{-7+4}{3}[/tex]
= [tex]\frac{-3}{3}[/tex]
= -1
