1. Let f (x) = x + 3 and g (x) = 3x + 5. Find f (g (4)) - g (f (4)) 2. Let f (x) = 5x^2 - 5. What is f (f (x)) ? 3. Let f (g (x)) = 3x + 3 and f (x) = x + 6. If g (x) = ax + b, compute a + b. 4. Let f (x) = 2x - 3 and g (f (x)) = 5 - 4x. Find g (4)

1. f (g (4)) - g (f (4)) = - 6

2. f (f (x)) = 125x^4 - 250x^2 + 120

3. a + b = 0

4. g (4) = - 9

Step-by-step explanation:

1.

First we need to find f (4) and g (4):

f (4) = 4 + 3 = 7

g (4) = 3*4 + 5 = 17

Then, we find g (f (4)) = g (7):

g (7) = 3*7 + 5 = 26

And we find f (g (4)) = f (17):

f (17) = 17 + 3 = 20

so f (g (4)) - g (f (4)) = 20 - 26 = - 6

2.

To find f (f (x)), we use the value of f (x) for every x in f (x):

f (f (x)) = 5 * (f (x)) ^2 - 5 = 5 * (5x^2 - 5) ^2 - 5 = 5 * (25x^4 - 50x^2 + 25) - 5

f (f (x)) = 125x^4 - 250x^2 + 120

3.

To find f (g (x)), we use the value of g (x) for every x in f (x):

f (g (x)) = g (x) + 6 = ax + b + 6 = 3x + 3

ax + (b+6) = 3x + 3 - > a = 3 and b = - 3

a + b = 3 - 3 = 0

4.

If we assume g (x) = ax + b, we have:

g (f (x)) = a * (2x - 3) + b = 2ax - 3a + b = 5 - 4x

2a = - 4 - > a = - 2

-3a + b = 5

6 + b = 5 - > b = - 1

g (x) = - 2x - 1

g (4) = - 2*4 - 1 = - 9