Answer :

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.


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