Question

Which of the function below is that inverse of f(x)=x^-25

Answer 1

g⁻¹(x) = ±√(x + 25)

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.