Question

If f (x) = 3x, g (x) = x + 4, and h (x) = x^2 - 1, find [fo(hog)] (1)

Answer 1

Explanation:

To find [fo(hog)] (1), we need to first evaluate the composition hog at x = 1, and then plug the result into f.

Let's start by evaluating hog at x = 1:

hog(x) = h(g(x)) = h(x + 4) = (x + 4)^2 - 1

So, hog(1) = (1 + 4)^2 - 1 = 24

Now we can evaluate f at hog(1):

f(hog(1)) = f(24) = 3(24) = 72

Therefore, [fo(hog)] (1) = 72.