Given the function f, g and h be defined by f(x)=2x-3, g(x)=3x sqaure-4 and h=sin(x). Find the formula defining the composition function h°f°g
f(x) = 2x - 3
g(x) = 3x^2 - 4
h(x) = sin(x)
Let k(x) = f°g (replace all instances of x in f(x) by g(x))
Then, k(x) = (2x - 3)°(3x^2 - 4) (replace the x in 2x by 3x^2 - 4)
k(x) = 2(3x^2 - 4) - 3
k(x) = 6x^2 - 11
Now let q(x) = h°k (replace all instances of x in h(x) by k(x))
Then q(x) = sin(x)°(6x^2 - 11) (replace the x in sin(x) by 6x^2 - 11)
q(x) = sin(6x^2 - 11)
And, q(x) = h°k = h°f°g
So, h°f°g = sin(6x^2 - 11)