Find the composite function fog(x)=f(gx)), given f(x)=x^2-1 and g(x)=3x+5

Question

Find the composite function fog(x)=f(gx)), given f(x)=x^2-1 and g(x)=3x+5

Answer 1

f(x) = x^2 -1

g(x) = 3x+ 5

replace g(x) with 3x+5

f(g(x)) = f(3x+5)

= (3x+5)^2 -1

= 9x^2 + 30x + 25 -1

= 9x^2 + 30x + 24

You could usually stop at this point or you can go further:

= 3(3x^2 +10x + 8)

f(g(x)) = 3(3x+4)(x+2) in integer factored form

Answer 2

f(g(x)) = (3x + 5)² - 1