# What is the meaning of a small o in between function names? i.e (f o g)

I am helping with homework.

I am stumped here - What is the meaning of the small round circle, or small "o" in question 19 (that I underlined) and question 20

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– pedja Oct 2 '11 at 17:31

It is function composition. If you have one function $f(x)$, and another function $g(x)$, then we can create a new function named $g\circ f$ (read as: "$g$ composed with $f$") that is defined as $$(g\circ f)(x)=g(f(x))$$ For example, if $f(x)=x+1$, and $g(x)=2x-1$, then $$(g\circ f)(x)=g(f(x))=g(x+1)=2(x+1)-1=2x+1$$
Use of this symbol makes it possible to efficiently write things like $(g\circ f)^{-1} = f^{-1}\circ g^{-1}$. – Michael Hardy Oct 2 '11 at 17:31
So does question 19 solve out to 16x^2 - 1 – Raj More Oct 2 '11 at 17:37
@RajMore It goes like $h(4x+1) = (4x+1)^2-2 = 16x^2+8x+1-2 = 16x^2+8x-1$. – user13838 Oct 2 '11 at 17:41