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.

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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 $f(x)cdot g(x) = (2x-1)cdot (3x+2) = 6x^2+x-2$.



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