Question

Find the composition of functions f ° g ° h. Given f(x) = 2x - 4, g(x) = sin(x), and h(x) = x².

Answer 1

To find the composition of the functions (f ∘ g ∘ h), apply h first, then g, and then f, resulting in the composed function (f ∘ g ∘ h)(x) = 2sin(x²) - 4.

Step-by-step explanation:

The student asked for the composition of functions f ∘ g ∘ h. Given that f(x) = 2x - 4, g(x) = sin(x), and h(x) = x², we need to apply each function in the correct order starting with the innermost function (h), then applying function g to the result of h, and finally applying function f to the result of g(h(x)).

First, we evaluate h(x):

h(x) = x²

Next, we substitute h(x) into g:

g(h(x)) = g(x²) = sin(x²)

Finally, we apply function f to the result of g(h(x)):

f(g(h(x))) = f(sin(x²)) = 2sin(x²) - 4

The composed function (f ∘ g ∘ h)(x) is therefore 2sin(x²) - 4.