Find the values of x for which the functions

Solution:

According to the question,

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

For what real numbers x, f (x) = g (x)

To satisfy the condition f(x) = g(x),

Should also satisfy,

3x2 – 1 = 3 + x

⇒ 3x2 – x – 3 – 1 = 0

⇒ 3x2 – x – 4 = 0

Splitting the middle term,

We get,

⇒ 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

⇒ x = 4/3, –1

Hence, for x = 4/3, –1, f (x) = g (x),

i.e., given functions are equal.