Question

Choose the inverse of y = x2 – 10x.

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Answer 1

y = x^2 − 10x = (x − 5)^2 − 25.
Solve for x: (x − 5)^2 = y + 25 so x − 5 = ±√(y + 25), hence x = 5 ± √(y + 25).

Swap x and y to write the inverse relation:
y = 5 ± √(x + 25), with domain x ≥ −25.

If you restrict the original to x ≥ 5 (right branch) the inverse is y = 5 + √(x + 25).
If you restrict the original to x ≤ 5 (left branch) the inverse is y = 5 − √(x + 25).

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