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The domain for which the functions defined by f (x) = 3x2 – 1 and g (x) = 3 + x are equal isA. {-1, 4/3} B. [-1, 4/3]C. (-1, 4/3)D. [-1, 4/3) |
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Answer» 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) |
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