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

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