Question

Which equation is the inverse of y = 7x2 – 10?

Answer 1

Interpret y = 7x^2 − 10 as y = 7x^2 − 10. To find the inverse swap x and y and solve for y:

x = 7y^2 − 10
7y^2 = x + 10
y^2 = (x + 10)/7
y = ± sqrt((x + 10)/7)

So the inverse relation is y = ±√((x+10)/7). To get an inverse function you must restrict the original domain so it is one-to-one. Common choices:

- If the original is restricted to x ≥ 0, the inverse is y = +√((x+10)/7) (domain x ≥ −10).
- If the original is restricted to x ≤ 0, the inverse is y = −√((x+10)/7) (domain x ≥ −10).