Simplify the composite function a ( b ( c ( x ) ) ) a\left(b\left(c\left(x\right)\right)\right) a ( b ( c ( x ) ) ) given the following: a ( x ) = − x 3 a\left(x\right)=-x^3 a ( x ) = − x 3 b ( x ) = cos ⁡ ( x ) b\left(x\right)=\cos\left(x\right) b ( x ) = cos ( x ) c ( x ) = x c\left(x\right)=\sqrt{x} c ( x ) = x <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

− cos ⁡ 3 x -\cos^3\sqrt{x} − cos 3 x <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

cos ⁡ x \sqrt{\cos x} cos x <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

x 3 cos ⁡ x x^3\sqrt{\cos x} x 3 cos x <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

− cos ⁡ x 3 -\cos x^3 − cos x 3

Combining Functions

0. Functions / Combining Functions / Problem 2

Problem 2

Simplify the composite function $a\left(b\left(c\left(x\right)\right)\right)$ given the following:
$a\left(x\right)=-x^3$
$b\left(x\right)=\cos\left(x\right)$ $c\left(x\right)=\sqrt{x}$

$\sqrt{\cos x}$

$x^3\sqrt{\cos x}$

$-\cos^3\sqrt{x}$

$-\cos x^3$

Learn this concept

Simplify the composite function a(b(c(x)))a\left(b\left(c\left(x\right)\right)\right)a(b(c(x))) given the following:a(x)=−x3a\left(x\right)=-x^3a(x)=−x3b(x)=cos(x)b\left(x\right)=\cos\left(x\right)b(x)=cos(x)c(x)=xc\left(x\right)=\sqrt{x}c(x)=x

Simplify the composite function $a\left(b\left(c\left(x\right)\right)\right)$ given the following:
$a\left(x\right)=-x^3$
$b\left(x\right)=\cos\left(x\right)$ $c\left(x\right)=\sqrt{x}$