i am at this time doing a surfacetoairnewyork.com problem and have come across an unfamiliar notation.A mini circle between $f$ and $h(x)$

The question ask me to uncover for "the functions $f(x)=2x-1$ and also $h(x)=3x+2$"

$$f circ h(x)$$

However, i can"t execute this together I carry out not recognize what the circle notation denotes to.Does it mean to multiply?


*

*

This notation method that you take it the calculation of $h$ and use it as the entry of $f$. When we are working v a specific $x$ value, we have the right to suggestively create $f(h(x))$ instead.

You are watching: What does an open circle mean in math

For circumstances if $f(z)=1/z$ and also $h(x)=2+3x$ climate $$(fcirc h)(x) = fig(h(x)ig) = f(2+3x) = frac12+3x.$$

(Note: i only supplied $z$ as the variable because that $f$ to prevent confusion; in practice the function does not treatment what that is input variable is named.)


*

The one $circ$ is the symbol because that composition of functions. In General, if you have two attributes $gcolon X ightarrow Y$ and $fcolon Y ightarrow Z$, then$fcirc g$ is a function from $X$ to $Z$. Because that $xin X$ one has $(fcirc g)(x) = f(g(x))$.

In your instance one has: $f(x) = 2x-1$, $g(x) = 3x+2$ and also $$(fcirc g)(x) = f(g(x)) = 2(g(x))-1 = 2(3x+2) -1 = 6x+3.$$You take the duty $g(x)$ and put the in ar of the $x$ in the duty $f$.

This is obviously different from $f(x)cdot g(x) = (2x-1)cdot (3x+2) = 6x^2+x-2$.


*

*

Thanks because that contributing response to surfacetoairnewyork.com Stack Exchange!

Please be sure to answer the question. Provide details and also share your research!

But avoid

Asking because that help, clarification, or responding to various other answers.Making statements based on opinion; earlier them up with referrals or personal experience.

Use surfacetoairnewyork.comJax to format equations. surfacetoairnewyork.comJax reference.

See more: Chicago Kiss Fm Jingle Ball 2016 Chicago, Photos: Iheartradio And 103

To learn more, watch our advice on writing good answers.


post Your price Discard

By clicking “Post her Answer”, girlfriend agree to our regards to service, privacy policy and also cookie plan


Not the price you're spring for? Browse various other questions tagged functions notation or asking your very own question.


Notation that a Unit Circle: go $S^1$ only mean a unit circle? Or walk it have actually something to carry out with symmetric groups?
site architecture / logo design © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.22.40552


your privacy

By clicking “Accept every cookies”, friend agree ridge Exchange can store cookies on your an equipment and disclose info in accordance v our Cookie Policy.