Question

Let g(x)=3x+2 and f(x)= x-2/3

Answer 1

Answer:

1.) 1 1/3 or 4/3

2.) 6

3.) 8

Step-by-step explanation:

Function composition substitutes more than just values or constants. It substitutes functions inside another function. Solve each expression by starting inner most and working to outermost.

1.) f(g(0))  = 1 1/3

Let g(x)=3x+2 and f(x)= x-2/3.

Begin with g(0) = 3(0) + 2 = 2.

Substitute x = 2 into f(x).

f(2) = (2) - 2/3 = 1 1/3

2.) g(f(2))  = 6

Let g(x)=3x+2 and f(x)= x-2/3.

Begin with f(2) = 2 - 2/3 = 1 1/3.

Substitute x = 1 1/3 into g(x).

g(1 1/3) = 3( 1 1/3) + 2 = 3(4/3) + 2 = 4 + 2 = 6

3.) g(g((0))

Let g(x)=3x+2.

Begin with g(0) = 3(0) + 2 = 2.

Substitute x = 2 into g(x).

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