Question

Let f(x)=9−8x‾‾‾‾‾‾√ .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 ? Select all that apply if more than one is appropriate. A. p(x)=−6x‾‾‾‾√ and q(x)=9+x
B. p(x)=9+x‾‾‾‾‾√ and q(x)=6x
C. p(x)=−x‾‾‾√ and q(x)=6x−9
D. p(x)=9−x‾‾‾‾‾√ and q(x)=6x
E. p(x)=x√ and q(x)=9−6x
F. p(x)=9−6x and q(x)=x√
G. All of the above
H. None of the above

Answer 1

Answer:

C, D and E

Step-by-step explanation:

Assuming  

f(x) = √(9−8x)

and the options are:

A. p(x) = √(-8x) and q(x)=9+x

B. p(x) = √(9+x) and q(x)=8x

C. p(x) = √(-x) and q(x)=8x−9

D. p(x)=√(9−x) and q(x)=8x

E. p(x)=√x and q(x)=9−8x

F. p(x)=9−8x and q(x)=√x

G. All of the above

H. None of the above

Substituting in f(x)=p(q(x)) we get:

A. √(-8(9+x)) = √(-72 - 8x)

B. √(9+(8x)) = √(9+8x)

C. √(-(8x−9 )) = √(-8x + 9)

D. √(9−(8x)) = √(9−8x)

E. √(9−8x )

F. 9−8(√x ) = 9 - 8√x