Question Video: Finding the Sum of Two Polynomial Functions Mathematics

If 𝑓(𝑥) = 𝑥 + 5 and 𝑔(𝑥) = 𝑥² − 2, then find and fully simplify an expression for (𝑓 + 𝑔)(𝑥).

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Video Transcript

If 𝑓 of 𝑥 equals 𝑥 plus five and 𝑔 of 𝑥 equals 𝑥 squared minus two, then find and fully simplify an expression for 𝑓 plus 𝑔 of 𝑥.

𝑓 plus 𝑔 of 𝑥 is a combination of functions. In fact, given two functions 𝑓 of 𝑥 and 𝑔 of 𝑥, 𝑓 plus 𝑔 of 𝑥 is simply their sum. Now, in this case, 𝑓 of 𝑥 is 𝑥 plus five plus 𝑔 of 𝑥 is 𝑥 squared minus two. So 𝑓 plus 𝑔 of 𝑥 is 𝑥 plus five plus 𝑥 squared minus two. The expression for 𝑓 plus 𝑔 of 𝑥 just needs to be simplified. And so we collect like terms. Five add negative two is three. So we get 𝑥 squared plus 𝑥 plus three. Given 𝑓 and 𝑔 then, 𝑓 plus 𝑔 of 𝑥 is 𝑥 squared plus 𝑥 plus three.

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