The image contains a problem where two functions are given:

• $f(x) = x - 3$
• $g(x) = 5x^2 - 3$

We are asked to find the composition of functions $f \circ g(x)$, which means we need to evaluate $f(g(x))$.

Solution for part (a): $f \circ g(x)$

1. Start with the function for $g(x)$: $g(x) = 5x^2 - 3$
2. Now substitute $g(x)$ into the function $f(x)$, i.e., replace $x$ in $f(x) = x - 3$ with $g(x)$: $f(g(x)) = g(x) - 3 = (5x^2 - 3) - 3$
3. Simplify: $f(g(x)) = 5x^2 - 6$

Thus, the solution for part (a) is: $f \circ g(x) = 5x^2 - 6$

Let me know if you would like help with other parts of the problem or further explanations.

Here are 5 related questions you can explore:

1. How do you calculate $g \circ f(x)$?
2. What is the composition of functions at a specific value, like $f(g(-1))$?
3. Can you explain the difference between $f \circ g(x)$ and $g \circ f(x)$?
4. How do you check if a composition of functions is invertible?
5. What happens if you switch the order of composition between two arbitrary functions?

Tip: When composing functions, always substitute the entire function for the variable in the outer function!