Question

Let f(x) = x + 3 and g(x) = 3x + 5. Find f(g(4)) - g(f(4))

Answer 1

First, we need to find g(4):

g(x) = 3x + 5
g(4) = 3(4) + 5
g(4) = 12 + 5
g(4) = 17

Next, we need to find f(g(4)):

f(x) = x + 3
f(g(4)) = f(17)
f(g(4)) = 17 + 3
f(g(4)) = 20

Now, we need to find f(4):

f(x) = x + 3
f(4) = 4 + 3
f(4) = 7

Finally, we can find g(f(4)):

g(x) = 3x + 5
g(f(4)) = g(7)
g(f(4)) = 3(7) + 5
g(f(4)) = 21 + 5
g(f(4)) = 26

Now we can calculate f(g(4)) - g(f(4)):

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