10 pts+ brainliest if correct
2 answers:
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Answer:
The options are endless.
You do have the following requirements to the letters asked about:
c=b (neither of these can be 0)
d=a
So here is one example:
Choose c=b=4 and d=a=9.
The functions will be:
and
Step-by-step explanation:
I'm going to assume my comment above.
In order for f and g to be inverse f(g(x)) has to give you x and g(f(x)) also has to give you x.
We want this to equal x.
This means we need the following to happen:
The first one happens when assuming b isn't 0 since you can't divide by 0.
The second one happens when the top is 0 because that is the only way a fraction will output you 0 is if the numerator is 0.
So we as well.
So this is what we need for f and g so that they are inverse:
since
and
Let's try to see if we get x when doing both f(g(x)) and g(f(x)).
We have confirmation that f(g(x))=x.
So and
are inverses for all choices c and d except when c is 0 since you are not allowed to divide by 0.
Your question says to insert numbers for c (=b) and d (=a).
So an example:
Let b=c=4 and d=a=9.
Let's try it:
These will be our functions with those choices for the constant variables:
and
We have f(g(x))=x. Check mark, there.