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

$$f circ h(x)$$

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

This notation way that you take it the calculation of $h$ and also use it as the entry of $f$. As soon as we space working v a certain $x$ value, we have the right to suggestively compose $f(h(x))$ 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 offered $z$ as the variable for $f$ to protect against confusion; in exercise the function does not care what that is input change is named.)

The one $circ$ is the symbol for composition the functions. In General, if you have actually two features $gcolon X ightarrow Y$ and $fcolon Y ightarrow Z$, then$fcirc g$ is a function from $X$ come $Z$. For $xin X$ 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 location of the $x$ in the duty $f$.

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

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Notation of a Unit Circle: walk $S^1$ only mean a unit circle? Or does it have something to do with symmetric groups?

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