Question

The domain for which the functions defined by f (x) = 3x² – 1 and g (x) = 3 + x are equal is

A. {-1, 4/3} 
B. [-1, 4/3]
C. (-1, 4/3)
D. [-1, 4/3)

Answer 1

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

To find: the domain of the given functions equal

Explanation: So the domain of a function consists of all the first elements of all the ordered pairs, i.e., x, so we have to find the values of x to get the required domain

The two given functions are equal, so

f (x) = g (x)

Substituting the values, we get

3x² – 1 = 3 + x

3x² – 1 - 3 – x = 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

x = 4/3, -1

Hence for x = 4/3, -1 f (x) = g (x), i.e., given functions are equal.

Hence the domain is = [-1, 4/3]

Hence the correct answer is option (B)