Suppose you have a function y fx such that the domain of fx

Suppose you have a function y = f(x) such that the domain of f(x) is 1 lessthanorequalto x lessthanorequalto 6 and the range of f(x) is -2 lessthanorequalto y lessthanorequalto 5. (e) Can you find constants B and C so that the domain of f(B(x - C)) is 7 lessthanorequalto x lessthanorequalto 8? Yes No Find the constants B and C, if they exist. (If an answer does not exist, enter DNE.) B = 1/4 C = -34 (f) Can you find constants A and D so that the range of Af(x) + D is 0 lessthanorequalto y lessthanorequalto 1? Yes No Find the constants A and D, if they exist. (If an answer does not exist, enter DNE.) A = D =

Solution

Solution:

A) B, C ?

for f(x) Then f(B(x-C))

and for this new function 7<=x<=8

from the second inequality

7-C<=x-C<=8-C

B(7-C)<=B(x-C)<=B(8-C)

this has to be as

So, B(7-C)=1

B(8-C)=5

solving the 2 equations we get

B=4

C=27/4

B) A and D ?

For Example The statement

3 y 6

or

3 f(x) 6

then

3A Af(x) 6A

then

3A+D Af(x)+D 6A+D

this has to be the same as

0 y 1 or

0 Af(x)+d 1

So, -3A+D=0

6A+D=1

solving the 2 equations

A=1/9

D=1/3