decomposition

Question

let f (x) = √(7-2x)

which of the following decompositions of f(x) = p(q(x)) into a pair of functions p (x) ( the outside function) and q (x) (the inside function) are correct?

1- p (x) = √(7-x) and q (x) =2x

2- p(x) = √-x and q (x) = 2x-7

3- p (x) = √(-2x) and q (x) = 7+x

4- p (x) = √x and q (x)= 7-2x

5- p(x)= √(7+x) and q (x) = 2x

6- p(x) = 7-2x and q(x) = √x

Answer 1

I would suggest to use p(q) notation instead of p(x), than it will be much easier to find correct answers:

 

1- p (q) = √(7-q) and q (x) =2x      correct, as you get after re-substitution: p (x) = √(7-2x)

2- p(q) = √-q and q (x) = 2x-7       correct, check  by re-substitution

3- p (q) = √(-2q) and q (x) = 7+x   not  correct, as you will get:  p (x) = √(-2(7+x))= √-14 -2x

4- p (q) = √q and q (x)= 7-2x         correct

 

5- p(q)= √(7+q) and q (x) = 2x       not correct

6- p(q) = 7-2q and q(x) = √x        not correct,