Question

Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x 2 Find F{G[H(2)]}. 27 71 121

Answer 1

Explanation:

h(2)= 2

g(2)= 3(2) + 2 = 6 + 2 = 8

f(8)= 2(8) - 1 = 16 - 1 = 15

Answer 2

27

Explanation:

Set up the composite result function.

F(G(H(x)))

Evaluate F(G(H(x))) by substituting in the value of H into G.

Multiply 3 by x^2

F(G(x2))=F(3x2+2)

Evaluate F(G(x)) by substituting in the value of G into F

F(3x2+2)=2(3x2+2)-1

Simplify each term.

Apply the distributive property.

F(3x2+2)=2(3x2)+2⋅2-1

Multiply 3 by 2

F(3x2+2)=6x2+2⋅2-1

Multiply 2 by 2

F(3x2+2)=6x2+4-1

Subtract 1 from 4

F(3x2+2)=6x2+3

Evaluate the result function by replacing x with 2 in the function.

6(2)2+3

Simplify the evaluated function.

Simplify each term.

Raise 2 to the power of 2

6⋅4+3

Multiply 6 by 4

24+3

27