Question

Find the functions a) f○g, b) g○f, c) f○f, and d)g○g and their domains
31.f(x)=x^2-1, g(x)=2x+1

Answer 1

the composition of two polynomials is again a polynomial, so the answer to "their domains" is "all real numbers" for ever question

Answer 2

How do you find the functions a-d

Answer 3

a) f(g) = g^2-1=(2x+1)^2-1
b) g(f)=2f+1=2(x^2-1)+1

Answer 4

Luckily I got that point but for a) they look like they simplified it further or in the back of the book they got 4x^2+4x and b)2x^2-1. Can you show me how they got those answers?

Answer 5

(a+b)^2=a^2+2ab+b^2
(2x+1)^2=4x^2+4x+1
(2x+1)^2-1=4x^2+4x

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

Answer 6

Ok now I see thankyou. : )op