Question

which equation is the inverse of (y = 7x^2 - 10)?

(y = \frac{pmsqrt{x + 10}}{7})

(y = pmsqrt{\frac{x + 10}{7}})

(y = pmsqrt{\frac{x}{7} + 10})

(y = \frac{pmsqrt{x}}{7} pm \frac{sqrt{10}}{7})

Explanation:

Swap variables to set up the inverse relation

$$ x = 7y^2 - 10 $$

Isolate the quadratic term

$$ x + 10 = 7y^2 \implies y^2 = \frac{x + 10}{7} $$

Solve for y using the square root property

$$ y = \pm\sqrt{\frac{x + 10}{7}} $$

Answer:

• (A) \(y = \frac{\pm\sqrt{x + 10}}{7}\)
• (B) \(y = \pm\sqrt{\frac{x + 10}{7}}\) (Correct answer)
• (C) \(y = \pm\sqrt{\frac{x}{7} + 10}\)
• (D) \(y = \frac{\pm\sqrt{x}}{7} \pm \frac{\sqrt{10}}{7}\)