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It looks like you're working with compositions of functions, based on the notation in the image. Here’s an interpretation of the expressions:

1. \( h \circ g (x) \) represents the composition of the functions \( h(x) \) and \( g(x) \), meaning \( h(g(x)) \). This is function \( g(x) \) being used as the input for function \( h(x) \).

2. \( (h \circ g)(x) \) is the same as the first expression, again representing the composition of \( h \) and \( g \), so \( h(g(x)) \).

3. \( (h \circ f)(-1) \) represents the composition of the functions \( h(x) \) and \( f(x) \), evaluated at \( x = -1 \), so this would be \( h(f(-1)) \).

If you know the specific forms of \( h(x) \), \( g(x) \), and \( f(x) \), I can help you evaluate these expressions further.

Would you like to provide the functions and get further details, or is there another part of the problem you'd like to explore?

Here are five follow-up questions:
1. What are the definitions of \( h(x) \), \( g(x) \), and \( f(x) \)?
2. Do you need help simplifying the compositions or evaluating them for specific values?
3. Should I help explain how to approach function composition in general?
4. Are you working on inverse functions as well, or just compositions?
5. Do you need assistance graphing the functions or understanding their behavior?

**Tip:** When working with function compositions, always start by substituting the innermost function and then proceed step by step.

Given functions h, g, and f, solve the compositions h ∘ g(x) and h ∘ f(-1).

Explore function composition with the expressions h ∘ g(x) and h ∘ f(-1). Learn how to substitute one function into another to simplify and evaluate these types of algebraic expressions. Suitable for students in Grades 10-12.

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