To find $(f \circ g \circ h)(x)$, we need to apply the composition of functions step by step. This notation means:

$(f \circ g \circ h)(x) = f(g(h(x)))$

Step 1: Apply $h(x)$

Given $h(x) = x^2$, we replace $h(x)$ in the expression: $g(h(x)) = g(x^2)$

Step 2: Apply $g(x)$

Given $g(x) = \sin(x)$, we replace $g(x^2)$: $g(x^2) = \sin(x^2)$

Step 3: Apply $f(x)$

Given $f(x) = 4x - 5$, we replace $f(g(x^2))$ with $f(\sin(x^2))$: $f(\sin(x^2)) = 4\sin(x^2) - 5$

Final Answer:

$(f \circ g \circ h)(x) = 4\sin(x^2) - 5$

Would you like more details on function composition or any other clarification?

Here are 5 related questions to expand on this:

1. How does function composition work in general?
2. What are the domains and ranges of the individual functions?
3. How would the result change if $h(x)$ were a different function?
4. Can you find the derivative of $(f \circ g \circ h)(x)$?
5. How would you evaluate $(f \circ g \circ h)(\pi)$?

Tip: When composing functions, work from the innermost function outward, applying each step sequentially.