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}`.