# How do you find the composition of function given f(x)=

How do you find the composition of function given $f\left(x\right)=\sqrt{x+8}$ and $g\left(x\right)=4x+1$
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Brenton Pennington
To complete a function composition, you must substitute one function in the place of x in the other. For example in $f\left(g\left(x\right)\right)$, you must plug function g into f.
$f\left(g\left(x\right)\right)=\sqrt{\left(4x+1\right)+8}$
$f\left(g\left(x\right)\right)=\sqrt{4x+9}$
When finding the composition of functions think of working from the inside to the outside. So, if you have f(g(h(x))), you plug h into g and then you plug the result from that calculation. When there is a number in the place of x, you must plug that number in for x and then work your way out.