Part 1. using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses. f(x)= x+a b g(x)=cx−d

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.

c = 1 and a,d can take any value such that a = d

Step-by-step explanation:

Function is a relative in which every element of domain has a unique image in the co-domain.

An inverse of a function exists if it is one-one and onto.

A function is onto if every element of the co-domain has a preimage in domain.

A function is said to be one to one if elements of the domain have different images in the co-domain.

On comparing and , we get c = 1 and a = d.

So, c = 1 and a,d can take any value such that a = d

its adding 5.5 each time

step-by-step explanation: