ns am at this time doing a civicpride-kusatsu.net problem and have come across an unfamiliar notation.A mini circle in between \$f\$ and \$h(x)\$

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) = fig(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\$.  Thanks because that contributing response to civicpride-kusatsu.netematics Stack Exchange!

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