Function Composition of Expressions

Function Composition of Expressions

Tuesday Feb. 16, 2021

When using expressions

Your base work is the same: start with the innermost function, evaluate that, and then plug in your answer to the outer function.

The only difference is that these answers will look a little goofy compared to what you're used to.

But, just work slowly and carefully and always trust your math over the way an answer looks.

LET'S TRY SOME!

 $f\left(x\right)=2x-5$  and  $g\left(x\right)=x^2-6x$  

• 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

 $f\left(x\right)=2x-5$  and  $g\left(x\right)=x^2-6x$  

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

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

• There is nothing else to simplify so you're done

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

NOW YOU TRY!

Open Ended

 $f\left(x\right)=2x-5$  and  $g\left(x\right)=x^2-6x$  
Find:  $g\left(f\left(x-3\right)\right)$  

Open Ended

 $f\left(x\right)=2x-5$  and  $h\left(x\right)=x+3$  
Find:  $h\left(f\left(x+2\right)\right)$  

Open Ended

 $f\left(x\right)=2x-5$  and  $h\left(x\right)=x+3$  
Find:  $f\left(h\left(x-7\right)\right)$  

Open Ended

 $g\left(x\right)=x^2-6x$  and  $h\left(x\right)=x+3$  
Find:  $g\left(h\left(x+1\right)\right)$