Question

If f(x)=x²-3 x+5 and g(x)=-2 x, find the following composition. (f°g)(2)

(f°g)(2)=__ (Simplify your answer.)

Answer 1

33

Explanation:

We have f(x) = x² - 3x + 5 and g(x) = -2x

We want to find (fog)(2) or f((g)(2))

To do so we plug in 2 into g(x) and then g(2) into f(x)

Plugging in 2 into g(x)

g(x) = -2x

g(2) = -2(2)

g(2) = - 4

Plugging in g(2) into f(x)

f(x) = x² - 3x + 5

g(2) = -4

f(-4) = (-4)² - 3(-4) + 5

==> simplify exponent

f(-4) = 16 - 3(-4) + 5

==> multiply -3 and -4

f(-4) = 16 + 12 + 5

==> combine like terms

f(-4) = 33

So (f°g)(2) = 33