i am at this time doing a rebab.net problem and also have come throughout an unfamiliar notation.A mini circle between $f$ and also $h(x)$

The concern ask me to find for "the features $f(x)=2x-1$ and $h(x)=3x+2$"

$$f circ h(x)$$

However, ns can"t do this as I perform not recognize what the one notation denotes to.Does it mean to multiply?



This notation means that you take the output of $h$ and also use it as the input of $f$. When we are working with a certain $x$ value, we can 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 exercise the role does not treatment what that is input variable is named.)


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

In your situation one has: $f(x) = 2x-1$, $g(x) = 3x+2$ and $$(fcirc g)(x) = f(g(x)) = 2(g(x))-1 = 2(3x+2) -1 = 6x+3.$$You take the role $g(x)$ and put it in place 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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