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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!

For f(x) = x - 3 and g(x) = 5x^2 - 3, find the following functions: a) f ∘ g(x).

Explore how to solve function composition problems with quadratic functions. This problem demonstrates how to find f ∘ g(x) when f(x) = x - 3 and g(x) = 5x^2 - 3, with a detailed step-by-step solution. Suitable for Grades 9-11.

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