Question

which equation is the inverse of (y = 9x^2 - 4)?

• (y = \frac{pmsqrt{x+4}}{9})
• (y = pmsqrt{\frac{x}{9}+4})
• (y = \frac{pmsqrt{x+4}}{3})
• (y = \frac{pmsqrt{x}}{3} + \frac{2}{3})

Explanation:

Swap variables to find the inverse relation

$$ x = 9y^2 - 4 $$

Solve for y

$$
LATEXBLOCK0
$$

Simplify the radical expression

$$ y = \frac{\pm\sqrt{x + 4}}{3} $$

Answer:

• (A) \(y = \frac{\pm\sqrt{x+4}}{9}\)
• (B) \(y = \pm\sqrt{\frac{x}{9}+4}\)
• (C) \(y = \frac{\pm\sqrt{x+4}}{3}\) (Correct answer)
• (D) \(y = \frac{\pm\sqrt{x}}{3} + \frac{2}{3}\)