Question

Find fg(x)

`f(x) = {x}^(2) + 2`

`g(x) = {x}^(2) + 6x + 11`
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Answer 1

f(g(x)) = x^4 + 12x^3 + 14x^2 -132x + 123

Explanation:

Here, we simply will place g(x) into f(x)

So every x in f(x) is replaced by g(x)

Thus, we have;

(x^2 + 6x + 11)^2 + 2

= (x^2+6x-11)(x^2 + 6x -11) + 2

= x^4 + 6x^3 -11x^2 + 6x^3 + 36x^2 - 66x -11x^2 -66x + 121 + 2

= x^4 + 12x^3 + 14x^2 -132x + 123