Question

let f(x)= sqrt(7-2x) Which of the following decompositions of f(x)=p(q(x)) into a pair of functions p(x) and q(x) is/are correct?
p(x)=sqrt(7-x) and q(x)=2x
p(x)=sqrt(7+x) and q(x)=2x
p(x)=7-2x and q(x)=sqrt(x)
p(x)=sqrt(-x) and q(x)=2x-7
p(x)=sqrt(x) and q(x)=7-2x
p(x)=sqrt(-2x) and q(x)=7+x

Answer 1

first one yes second no third no fourth yes fifth yes last one no all you have to do is take whatever they give you for q(x) and plug it into x in p(x) and see if it is the same as f(x) so for instance on the first one you have q(x) = 2x so wherever you have x in p(x) you plug in 2x instead so you have p(2x)=sqrt(7-(2x))

Answer 2

which is the same as f(x)