Question

Find the domain for which the functions

f (x) = 2x² – 1 and g (x) = 1 – 3x are equal.

Answer 1

For  f(x) = g (x)

⇒ 2x² – 1 = 1 – 3x

⇒ 2x² + 3x – 2 = 0

⇒ 2x² + 4x – x – 2 = 0

⇒ 2x (x + 2) – 1 (x + 2) = 0

⇒ (2x – 1) (x + 2) = 0

Thus domain for which the function f(x) = g (x) is {1/2, -2}