Question

The domain for which the functions f(x) = 3x² −1 and g(x) = 3 + x are equal is __________ .

Answer 1

f(x) = 3x² − 1
g(x) = 3 + x
Given:- f(x) = g(x)
i.e 3x² − 1 = 3 + x
3x² − x − 1 − 3 = 0
3x² − x − 4 = 0
3x² + 3x − 4x − 4 = 0
3x(x + 1) − 4 (x + 1) = 0
(3x − 4) (x + 1) = 0
i.e x = $\frac{4}{3}$ or x = −1
∴ Domain for which f(x) and g(x) are equal is $\left\{-1,\frac{4}{3}\right\}$