Let f(x)=√3−8x . 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) is/are correct ?

Question

A. p(x)= 3−8x p(x)=3−8x and q(x)=√x q(x)=x

B. p(x)=√3+x p(x)=3+x and q(x)=8x q(x)=8x

C. p(x)=√−x p(x)=−x and q(x)=8x−3 q(x)=8x−3

D. p(x)=√−8x p(x)=−8x and q(x)=3+x q(x)=3+x

E. p(x)=√x p(x)=x and q(x)=3−8x q(x)=3−8x

F. p(x)=√3−x p(x)=3−x and q(x)=8x q(x)=8x

Answer 1

f(x) = sqr3 -8x or did the problem intend to read sqr(3-8x)?

a) p(x)= 3-8x, q(x) = sqrx

p(q(x)) = 3-8sqrx which doesn't = f(x), no matter how the problem is interpreted

b) p(x) = sqr3 +x, q(x) =8x

p(q(x)) = sqr3 + 8x does Not = f(x) as written or under the 2nd interpretation

c) p(x) = sqr(-x), q(x)= 8x-3

p(q(x)) = sqr(-(8x-3)) = sqr(-8x+3)= sqr(3-8x) which = f(x) under the 2nd interpretation

d) p(x) = sqr(-8x), q(x) = 3+x

p(q(x)) = sqr(-8(3+x)) = sqr(-24-8x) which doesn't equal f(x) with either interpretation

same with p(x) = -8x

e) p(x) = sqr(x), q(x) = 3-8x

p(q(x)) = p(3-8x) = sqr(3-8x) Does = f(x) under the 2nd interpretation

f) p(x) = sqr3 -x, q(x) = 8x

p(q(x)) = p(8x) = sqr3 -8x = f(x) as written, the 1st interpretation.

f) looks like the correct answer, if f(x) = (sqr3) -8x

That's how PEMDAS, order of operations would interpret the problem, as written.

. Unless, the problem was really intended to have f(x) = sqr(3-8x)

then e) or c) is the correct answer

a,b, or d are false no matter how the problem is interpreted.

While f) is technically correct the way the problem is written,

a feeling, a hunch is that you want the 2nd interpretation and c) and e)