Question

Find the value of $q\left(p\left(5\right)\right)-p\left(q\left(5\right)\right)$ if $p\left(x\right)=x^2-4x+8$ and $q\left(x\right)=x-3$

• A. $10$
• B. $4$
  
• C. $-6$
  
• D. $6$
  

Answer 1

The correct option is D $6$

Given, $p=x^2-4x+8$

$\therefore p\left(5\right)=25-20+8=13$

Also given, $q\left(x\right)=x-3$

$\therefore q\left(5\right)=2$

Now $p\left(q\right(5\left)\right)=p\left(2\right)=2^2-4\cdot 2+8=4$

And, $q\left(p\right(5\left)\right)=q\left(13\right)=13-3=10$.

Therefore $q\left(p\right(5\left)\right)-p\left(q\right(5\left)\right)=10-4=6$