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Eliza Norton
Mathematics
5 May, 15:09
What is the inverse of f (x) = (x-2) ^3
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Hailey Pugh
5 May, 15:36
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g⁻¹ (x) = 2 + ∛x
Step-by-step explanation:
g (x) = (x - 2) ³ Rename g (x) as y
y = (x - 2) ³
Solve for x:
y = (x - 2) ³ Multiply each side by 3
∛y = x - 2 Add 2 to each side
∛y + 2 = x
x = ∛y + 2 Switch x and y
y = ∛x + 2 Rename y as g inverse
g⁻¹ (x) = 2 + ∛x
See the graphs of g (x) and g⁻¹ (x) below.
g (x) is the red line. g⁻¹ (x) is the blue line.
Each graph reflects the other about the dashed line representing the function y = x.
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