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Numerade Educator

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Problem 39 Medium Difficulty

Find $ f \circ g \circ h $.

$ f(x) = 3x -2 $ , $ g(x) = \sin x $ , $ h(x) = x^2 $

Answer

$$(f \circ g \circ h)(x)=f(g(h(x)))=f\left(g\left(x^{2}\right)\right)=f\left(\sin \left(x^{2}\right)\right)=3 \sin \left(x^{2}\right)-2$$

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Video Transcript

we have functions F, g and H, and we're going to find f of g of h. Another way to write that is f of G of h of X like this. So that shows that we're going to have a chav X as the inside function on its going inside G. So we're taking X squared and we're substituting it in for X in the G function, So g of h of X is sign of X squared. That whole thing is going into the F function. So we're taking the sign of X squared and we're substituting it in for X in the F function, and that's going to give us three times the quantity sign of X squared minus two.