College algebra

Question

If f(x) = x+4 and g(x) = 2x2-x-1, evaluate the composition (g o f)(2).

Answer 1

Answer 2

Hello, thank you for taking the time to post your question!

(g o f)(2) means taking g(f(2))

So to start with I would find f(2)

f(2) = 2 + 4 = 6

then you can plug that value into g(x)

g(6) = 2(6)^2 – 6 – 1

=2(36) – 6 – 1

=72 – 6 – 1

=65

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 3

f(x) =x+4

g(x) = 2x^2-x-1

(fog)(x) = f(g(x))

= f(2x^2-x-1)

= 2x^2-x-1+4

= 2x^2-x+3

(fog)(2) = 2(2)^2 -2+3

= 8-2+3 = 9

or g(2) = 2(2^2)-2-1 = 8-3=5

f(g(2)) = f(5) = 5+4 = 9

do the same for (gof)(2)

g(f(x)) = g(x+4) = 2(x+4)^2 -x -1

=2(x^2 +8x +16)-x-4-1

= 2x^2 +16x+32- x-5

=2(2^2) +16(2) -2+27

=8+32+25= 65

or

f(x)=x+4

f(2) = 2+4 =6

g(f(2)) = g(6) = 2(36)^2 -6-1 = 72-7=65

f(g(2)) = 9

g(f(2))=65