kejpsy

2022-01-23

What is the continuity of the composite function $f\left(g\left(x\right)\right)$ given $f\left(x\right)=\mathrm{sin}x$ and $g\left(x\right)={x}^{2}$?

pacetfv

Expert

$g\left(x\right)={x}^{2}$, so $f\left(g\left(x\right)\right)$
$f\left(x\right)=\mathrm{sin}x$
rep. x with $g\left(x\right)$, aka ${x}^{2}$
$f\left(g\left(x\right)\right)={\mathrm{sin}x}^{2}$

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