Building Functions from Functions

Given the functions f(x) = 2x + 3 and g(x) = x^2 - 1, find the composition of f(g(x)).

• 4x^2 + 1

• 2x^2 - 1

• 2x^2 + 1

• 4x + 1

If h(x) = 4x - 5 and k(x) = 2x + 1, what is the composition of h(k(x))? Simplify your answer.

• 3x + 2

• 10x - 6

• 8x - 1

• 6x - 4

Find the composition of the functions f(x) = 3x + 2 and g(x) = 2x - 1.

• 6x + 3

• 5x + 2

• 4x + 1

• 7x + 4

Given the functions f(x) = x^2 + 1 and g(x) = 2x - 3, calculate the composition of g(f(x)).

• 4x^2 - 3

• x^2 + 2x - 3

• 2x^2 - 1

• 4x^2 + 2x - 3

If h(x) = 5x + 2 and k(x) = x^2 - 4, what is the composition of k(h(x))? Simplify your answer.

• (5x + 2)^2 - 4

• (5x + 2) - 4

• (5x + 2)^2 + 2

• (5x + 2)^2 + 4

Find the composition of the functions f(x) = 2x + 1 and g(x) = 3x - 2.

• 5x + 1

• 6x + 1

• 6x - 3

• 5x - 3

Given the functions f(x) = x^2 - 2 and g(x) = 3x + 4, calculate the composition of f(g(x)).

• (3x + 4)^2 - 4

• (3x + 4)^2 + 4

• (3x + 4)^2 - 2

• (3x + 4)^2 + 2

If h(x) = 2x - 3 and k(x) = x^2 + 5, what is the composition of h(k(x))? Simplify your answer.

• 4x^2 + 2

• x^2 + 2x + 2

• 4x^2 + 7

• 2x^2 + 7

Find the composition of the functions f(x) = 4x + 3 and g(x) = 2x - 1.

• f(g(x)) = 4(2x - 1) + 3 = 8x - 4 - 3 = 8x - 7

• f(g(x)) = 4(2x - 1) + 3 = 8x - 4 + 3 = 8x - 1

• f(g(x)) = 4(2x - 1) + 3 = 8x - 4 + 3 = 8x + 2

• f(g(x)) = 4(2x - 1) + 3 = 8x - 4 + 3 = 8x + 4

Given the functions f(x) = 2x^2 + 1 and g(x) = x - 3, calculate the composition of g(f(x)).

• 2x^2 + 3

• 2x^2 - 3

• 2x^2 + 2

• 2x^2 - 2