Question

Use f(x) = 2x + 5 and g(x) = x^2-1 to determine the following( simplified where possible):
(g * f)(3)

Answer 1

(g*f)(3)
= g(3) * f(3)
= (3^2-1)*(2*3+5)
= ...

Answer 2

So for (g*f)(3) the answer is 88, right. I have two other:
(f + g)(2), the answer would be 12, right and
for last qs: f(g(x)), I got 2x^3 + 5x^2 - 2x -5

Could you please clarify steve if these qs are right.
Thanks

Answer 3

f(x) = 2x + 5 and g(x) = x^2-1

the f(g(x))
= f(x^2 - 1)
= 2(x^2 - 1) + 5
<b>f(g(x)) = 2x^2 - 2 + 5 = 2x^2 + 3</b>

check: try x = 6
g(6) = 36-1 = 35
f(35) = 2(35) + 5 = 75

in my answer of
f(g(x)) = 2x^2 + 3
f(g(6)) = 2(36) + 3 = 75

Answer 4

you did (f*g)(x), not (f◦g)(x) = f(g(x))