Question

What symbol represents the composition of a function? How do we rewrite f(g(3)) using the composition symbol?

a) ∘; f∘g(3)
b)×; f×g(3)
c) ⋅; f⋅g(3)
d) ⊕; f ⊕g(3)

Answer 1

The symbol for composition of a function is ∘, so f(g(3)) is written as f∘g(3). This notation means you apply g to 3 and then f to the result of g.

Step-by-step explanation:

The symbol that represents the composition of a function in mathematics is the small circle (∘). When composing two functions, say f and g, the composition is written as f∘g. This means that you first apply function g and then apply function f to the result. Rewriting f(g(3)) using the composition symbol would therefore yield the notation f∘g(3).

Here is how you translate f(g(3)) into a composition notation step-by-step:

1. 
   
3. Identify the inner function, which is g in this case.
4. 
   
6. Identify the outer function, which is f.
7. 
   
9. Write the composition as the outer function composed with the inner function using the composition symbol: f∘g.
10. 
    
12. Apply the argument 3 to the composed functions: f∘g(3).

The correct answer is: a) ∘; f∘g(3)