$f \circ g (x)$ is defined as $f (g (x))$

your answer is correct , please use equation editor to type set equations properly

your answer is correct , please use equation editor to type set equations properly

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The functions mapping $R$ into $R$ are defined as :

$f\left(x \right)=x^{3} - 4x, g\left(x \right)=\frac{1}{x^{2}+1}$ and $h\left(x \right)=x^{4}.$

Then find the value of the following composite functions :

$h_{o}g\left(x \right)$ and $h_{o}g_{o}f\left(x \right)$

- $\left ( x^{2}+1 \right )^{4}$ and $\left [ \left ( x^{3}-4x \right )^{2}+1 \right ]^{4}$
- $\left ( x^{2}+1 \right )^{4}$ and $\left [ \left ( x^{3}-4x \right )^{2}+1 \right ]^{-4}$
- $\left ( x^{2}+1 \right )^{-4}$ and $\left [ \left ( x^{2}-4x \right )^{2}+1 \right ]^{4}$
- $\left ( x^{2}+1 \right )^{-4}$ and $\left [ \left ( x^{3}-4x \right )^{2}+1 \right ]^{-4}$