Let f(x) = x2 − 9 and g(x) = 3x − 4. Find the value, if possible. (If not possible, enter IMPOSSIBLE.) (f · g)(−3)

Question

(f · g)(−3) =

Answer 1

f(x) = x² - 9 and g(x) = 3x - 4

f(-3) = (-3)² - 9 = 0

g(-3) = 3(-3) - 4 = -13

So, (f • g)(-3) = [f(-3)][g(-3)] = (0)(-13) = 0

Answer 2

f(X) = X² - 9

g(X) = 3X-4

(f•g)(x)

=f(g(x))

put g(x) in place of X in f(X) = X² - 9

(f•g)(x) =f(g(x))

= (3X-4)² -9

= (3X-4) (3X-4) -9

= 9X² -24X +16 -9

= 9X² -24X + 7

-b ± √(b² -4ac

2a

a=9, b = -24, c =7

-(-24) ± √ (-24)² -4(9)(7))

2(9)

= [24 ± √(576 -252)] / 18

= (24 ± √324 )/ 18

= (24 ± 18) / 18

= (24-18)/18 or (24+18)/18

=6/18 or 42/18

=1/3, or 7/3

If you put 1/3 and 7/3 into the quadratic equation, it satisfies it with 0.