Function Composition of Expressions

Find f(g(2x))

First, plug in 2x into your g function

 $g\left(2x\right)=\left(2x\right)^2-6\left(2x\right)$  

 $g\left(2x\right)=\left(2x\right)\left(2x\right)-6\left(2x\right)$  

 $g\left(2x\right)=4x^2-12x$  

since there's nothing else to simplify  $4x^2-12x$  will be evaluated at f(x) now... which will be in the next slide

 $f\left(4x^2-12x\right)=2\left(4x^2-12x\right)-5$ 

 $f\left(4x^2-12x\right)=8x^2-24x-5$  

There is nothing else to simplify so you're done

 $f\left(g\left(x\right)\right)=8x^2-24x-5$