Let f : N → X : f(x) = 4x^2 + 12x + 15. Then, f^-1(y) = ?

Question

Mark (√) against the correct answer in the following: 

Let f : N → X : f(x) = 4x² + 12x + 15. Then, f^-1(y) = ?

A. \(\frac{1}{2}(\sqrt{y-4}+3)\) 

B. \(\frac{1}{2}(\sqrt{y-6}-3)\)

C. \(\frac{1}{2}(\sqrt{y-4}+5)\)

D. None of these

Answer 1

Correct Answer is (B) \(\frac{1}{2}(\sqrt{y-4}+3)\)

f(x) = 4x² + 12x + 15

⇒y = 4x² + 12x + 15

⇒y = (2x + 3)² + 6

⇒√(y - 6) = 2x + 3

⇒ \(\frac{1}{2}(\sqrt{y-4}+3)\) = x

f^-1(y) =\(\frac{1}{2}(\sqrt{y-4}+3)\)