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
