Mathematics, 29.07.2019 22:20 bgallman153p71edg

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

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Answer from: jahnoibenjamin

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:

$f(x)=\frac{x+9}{4}$ and

g(x)=4x-9

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.

f(g(x))

f(cx-d)

$\frac{(cx-d)+a}{b}$

$\frac{cx-d+a}{b}$

$\frac{cx+(-d+a)}{b}$

$\frac{cx}{b}+\frac{-d+a}{b}$

We want this to equal x.

This means we need the following to happen:

$\frac{c}{b}=1 \text{ and } \frac{-d+a}{b}=0$

The first one happens when c=b 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 d=a as well.

So this is what we need for f and g so that they are inverse:

$f(x)=\frac{x+d}{c}$ since d=a and c=b

g(x)=cx-d

Let's try to see if we get x when doing both f(g(x)) and g(f(x)).

f(g(x))

f(cx-d)

$\frac{(cx-d)+d}{c}$

$\frac{cx-d+d}{c}$

$\frac{cx}{c}$

We have confirmation that f(g(x))=x.

g(f(x))

$g(\frac{x+d}{c})$

$c(\frac{x+d}{c})-d$

x+d-d

So $f(x)=\frac{x+d}{c}$ and g(x)=cx-d 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:

$f(x)=\frac{x+9}{4}$ and g(x)=4x-9

f(g(x))

f(4x-9)

$\frac{(4x-9)+9}{4}$

$\frac{4x}{4}$

We have f(g(x))=x. Check mark, there.

g(f(x))

$g(\frac{x+9}{4})$

$4(\frac{x+9}{4})-9$

x+9-9

Answer from: mahagonylabeyta

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.

$y=f(x)=x+a\\y=x+a\\x=y-a\\f^{-1}(x)=x-a$

On comparing $f^{-1}(x)=x-a$ and g(x)=cx-d , we get c = 1 and a = d.

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

Answer from: Quest

Idon’t know but hope this you

Answer from: Quest

x = 25/2304

step-by-step explanation:

Can someone ? during the day, lola's dog is tied by rope to a tree in the center of her yard. the

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Part 1. using the two functions listed below, insert numbers in place of the letters a, b, c, and d...