Given f (x ) = x2 + 3x + 2 and g (x ) = x + 1, perform the indicated operations. In the space provided, type the answer in descending order. (fg)(x)

Answer 1

This is a composite function, with f(x) being the "outer" function and g(x) being the "inner" function.

So we say f(g(x)) is just f(x) but instead of plugging x in as the variable in f(x), we plug in g(x) instead.

f(x) = x² + 3x + 2, but because of that inner function, g(x), we say:

f(g(x) = (x+1)² + 3(x+1) + 2.

Expanding this:

= (x² + 2x + 1) + 3x + 3 + 2

= x² + 5x + 6

= (x+2)*(x+3)