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) = fig(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\$.  Thanks for contributing solution to rebab.net Stack Exchange!

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