Given f(x) = x2 + x + 1, g(x) = x – 2

Question

Given f(x) = x² + x + 1, g(x) = x – 2, find:

a.      (f ° g)(x)

b.      (g ° f)(x)

c.      (f ° g)(-1)

d.      (g ° f)(-1)

Answer 1

These used to confuse me, too!

So, if we were looking for f(3), we'd substitute 3 for x, right?

f(3) =3² + 3 + 1 = 9 + 3 + 1 = 13

We can find a value because we are given a value to substitute for x.

With f °g(x), we substitute g(x) for x. Since g(x) = x - 2...

f ° g(x) = (x - 2)² + (x - 2) + 1 = x² - 4x + 4 + x - 2 + 1 = x² - 3x - 1

Now, g(-1) = -1 - 2 = -3, so f ° g(-1) = f(-2) = (-2)² + (-2) + 1 = 4 - 2 + 1 = 3

The rest are on you.

Answer 2

a) (fog)(x) is found by substituting x-2 for x in f(x) = (x-2)^2 + (x-2) + 1

b) (gof)(x) is found by substituting x^2+ x + 1 for x in g(x) = x^2 + x + 1 - 2

c) (fog)(-1) is found by substituting -1 for x in x-2, then substituting the result for x in x^2 + x + 1

d) (gof)(-1) is found by substituting -1 for x in x^2 + x + 1, then substituting the result for x in x-2