Stuck with functions

Question

I was doing home work but I am stuck with some questions, here is the question with subparts,

enter image description here

Now I am stuck with what does $(2)$, $(x)$ and $(y)$ mean in these questions? For example, (a) $(f \circ g)(2)$ What is $(2)$ here?

Please help me out.

Thanks

These are parameters to the functions. Recall that a function is an object that takes input (in your case, some number) and produces output. For example, $g$ takes a number and returns its square.
Function composition ($\circ$) is an operation that takes two functions and produces a function obtained by running the function in succession. For example, composing $f$ and $g$ in one order produces a function $h(w) = w^2 - 1$, and in the other order it produces the function $i(w) = (w-1)^2$.
You can also compose a function with itself, for example $g \circ g$ means apply $g$ and then apply it again, i.e. square the input and then square it again. So in total $(g \circ g)(T) = g(T^2) = (T^2)^2 = T^4$.

Américo Tavares · Accepted Answer · 2011-08-26 15:01:41Z

up vote 5 down vote accepted

2 in $(f \circ g)(2)$ is where the function $g$ is evaluated. $$(f \circ g)(2)=f(g(2))=f(2^2)=f(4)=4-1=3.$$

answered Aug 26 '11 at 15:01

Américo Tavares
20.7k334105

Thankyou so very much for the answer. – Fahad Uddin Aug 26 '11 at 15:22

1

@fahad: Glad I could help. – Américo Tavares Aug 26 '11 at 15:32

1 Answer