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

Let $A=B=C=\Bbb R$, and let $f:A\to B,g:B\to C$ be defined by $f(a)=a-1$ and $g(b)=b^2$. Find

$\text{(a)}\,\,\,\,(f\circ g)(2)\qquad\qquad\text{(b)}\,\,\,\,(g\circ f)(2)$

$\text{(c)}\,\,\,\,(g\circ f)(x)\qquad\qquad\text{(d)}\,\,\,\,(f\circ g)(x)$

$\text{(e)}\,\,\,\,(f\circ f)(y)\qquad\qquad\,\text{(f)}\,\,\,\,(g\circ g)(y)$

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

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    Thanks alot. That was full of knowledge :)2011-08-26

1 Answers 1

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

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    @fahad: Glad I could help.2011-08-26