Question

Algebra 2B U2 L6 Function Operations practice 8-10

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

8 f(g(0))

A 0
B -2/3
C 1
D -1

9 g(f(2))

A 1
B 0
C 2
D 1/3

10 g(g(0))

A 0
B 8
C 6
D 2​

Answer 1

Answer:

1) f(g(0)) = 0

2)  g(f(2)) = 2

3)  g(g(0)) = 8

Step-by-step explanation:

Here, the given functions are:

g(x)  =  3 x +2 and f(x)=  (x-2)/3

1. Now, f(g(x))  =   f(3x+2)

Also,  f(3x+2) = (3x+2 -2) /3 = x

So, f(g(x)) = x

⇒ f(g(0)) = 0

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

or, g(f(x)) =   x

⇒  g(f(2)) =   3((2)-2/3) +2   = 2  

or, g(f(2)) = 2

3.  g(g(0)= g( 3 (0) +2)  = g(2)

Now, g(2)  = 3(2) +  2 = 6 +  2 = 8

or, g(g(0)) = 8