Question:
Find the values of x for which the functions
f (x) = 3x2 – 1 and g (x) = 3 + x are equal
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.