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

1) f(g(0)) = 0

2) g(f(2)) = 2

3) g(g(0)) = 8

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