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Vladimir79 [104]
4 years ago
10

F(x)=x^2+3 and g(x)=x^2-4 what is (gof)(x)

Mathematics
1 answer:
fenix001 [56]4 years ago
4 0

For this case we have the following functions:

f (x) = x ^ 2 + 3\\g (x) = x ^ 2-4

By definition of composition of functions, we have to:

(g_ {o} f) (x) = g (f (x))

So:

g (f (x)) = (x ^ 2 + 3) ^ 2-4 = (x ^ 2) ^ 2 + 2 (x ^ 2) (3) + 3 ^ 2-4 = x ^ 4 + 6x ^ 2 + 9-4=x^4+6x^2+5

Thus, we have to:

(g_ {o} f) (x) = x ^ 4 + 6x ^ 2 + 5

Answer:

(g_ {o} f) (x) = x ^ 4 + 6x ^ 2 + 5

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