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- #1

a) Find constants B and C so that the domain of f(B(x − C)) is 8 ≤ x ≤ 9

B=

C=

b) Find constants A and D so that the range of Af(x) + D is 0 ≤ y ≤ 1

A=

D=

I'm working on composition of functions and completely lost at this point.

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- Thread starter
- #1

a) Find constants B and C so that the domain of f(B(x − C)) is 8 ≤ x ≤ 9

B=

C=

b) Find constants A and D so that the range of Af(x) + D is 0 ≤ y ≤ 1

A=

D=

I'm working on composition of functions and completely lost at this point.

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- #2

I have moved your topic from the Analysis forum as this is a Pre-calculus topic.

For the first problem, I would begin with the function's new domain:

\(\displaystyle 8\le x\le9\)

Now, assuming $B$ is positive, can you algebraically get $B(x-C)$ in the middle, and then equating the end-points to the originals, you will have two equations in two unknowns?