Find the values of x for which the functions

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

Given: f and g functions defined by f (x) = 3x² – 1 and g (x) = 3 + x

To find: For what x, f (x) = g (x)

Explanation: to satisfy the condition f(x) = g(x), the given real functions should be equal

i.e., 3x² – 1 = 3 + x

⇒ 3x² –x-3-1 = 0

⇒ 3x² –x-4 = 0

We will find the solution by splitting the middle term, i.e.,

⇒ 3x² + 3x-4x-4 = 0

⇒ 3x(x + 1)-4(x + 1) = 0

⇒ (3x-4)(x + 1) = 0

⇒ 3x-4 = 0 or x + 1 = 0

⇒ 3x = 4 or x = -1

Hence for , f (x) = g (x), i.e., given functions are equal.