Answer:
if f(x) = 3x, g(x) = x+4, and h(x) = x²-1, Find [h•(f•g)](3)
{h • (f • g)}(3) = 440
Explanation:
To find {h • (f • g)}(3), we need to first evaluate the innermost function, f • g, then substitute the result into the outer function, h, and finally evaluate the resulting expression at x = 3.
Let's start by finding f • g:
f • g = f(g(x))
Substitute g(x) into f(x):
f • g = f(x + 4)
Now substitute f(x) into the above expression:
f • g = 3(x + 4)
Simplify:
f • g = 3x + 12
Now we can substitute this result into h(x):
h • (f • g) = h(3x + 12)
Substitute x = 3 into the above expression:
h • (f • g) = h(3(3) + 12)
Simplify inside the parentheses:
h • (f • g) = h(9 + 12)
Simplify further:
h • (f • g) = h(21)
Now let's evaluate h(21):
h(x) = x² - 1
h(21) = (21)² - 1
Simplify:
h(21) = 441 - 1
Final result:
{h • (f • g)}(3) = 440