Answer:
g⁻¹(x) = ±√(x + 25)
Step-by-step explanation:
g(x) = x² - 25 Rename g(x) as y
y = x² - 25
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Solve for x
y = x² - 25 Add 25 to each side
y + 25 = x² Take the square root of each side
x = ±√(y + 25) Switch x and y
y = ±√(x + 25) Rename y as g inverse
g⁻¹(x) = ±√(x + 25)
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See the graphs of g(x) and g⁻¹(x) below.
g(x) is the red line. g⁻¹(x) is the purple line.
Each graph reflects the other about the dashed line representing the function y = x.
