Question

question 1) Given: F(x) = 3x^2 + 1, G(x) = 2x - 3, H(x) = x

Find: F(G(x)) =

Question 2)

Given: F(x) = 3x^2 + 1, G(x) = 2x - 3, H(x) = x

Find: H -1 (x) =

Answer 1

Question 1)

Given: F(x) = 3x^2 + 1, G(x) = 2x - 3, H(x) = x

F(G(x)) = 3(2x - 3)^2 + 1

F(G(x)) =3(4x^2 - 12x + 9) + 1

F(G(x)) = 12x^2 - 36x + 27 + 1

F(G(x)) =12x^2 - 36x + 28

Question 2)

Given: F(x) = 3x^2 + 1, G(x) = 2x - 3, H(x) = x

H -1 (x) = x (inverse)