If f(x) = 2x + 5 and g(x) = 8-3x^2, what is the value of f(g(4)) - g(f(4))?
To find the value of f(g(4)) - g(f(4)), we need to substitute g(4) and f(4) into the functions and then perform the arithmetic operations.
First, let's find g(4):
g(x) = 8 - 3x^2
Substituting x = 4, we get:
g(4) = 8 - 3(4^2)
= 8 - 3(16)
= 8 - 48
= -40
Now let's find f(4):
f(x) = 2x + 5
Substituting x = 4, we get:
f(4) = 2(4) + 5
= 8 + 5
= 13
Now we can substitute g(4) and f(4) into the expression f(g(4)) - g(f(4)) and calculate the value:
f(g(4)) - g(f(4)) = f(-40) - g(13)
Substituting the values we found:
f(g(4)) - g(f(4)) = f(-40) - g(13)
= 2(-40) + 5 - (8 - 3(13^2))
= -80 + 5 - (8 - 3(169))
= -80 + 5 - (8 - 507)
= -80 + 5 - (-499)
= -75 + 499
= 424
Therefore, the value of f(g(4)) - g(f(4)) is 424.