What is the combined function of fx and gx when fx = x^2 + 3x + 4 and gx = x + 5?

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To find the combined function fx(gx), we start with the two given functions:

1. fx: fx(x) = x2 + 3x + 4

2. gx: gx(x) = x + 5

First, we will substitute gx(x) into fx(x). This means wherever we see an x in the function fx, we will replace it with gx(x).

Let’s proceed with the substitution:

fx(gx) = fx(x + 5)
= (x + 5)2 + 3(x + 5) + 4

Now we’ll expand and simplify:

= (x2 + 10x + 25) + (3x + 15) + 4
= x2 + 10x + 25 + 3x + 15 + 4
= x2 + (10x + 3x) + (25 + 15 + 4)
= x2 + 13x + 44

The resulting combined function is:

fx(gx) = x2 + 13x + 44

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