Mathematics, 20.12.2019 19:31, ndnx

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

next: show your work to prove that the inverse of f(x) is g(x).

then: show your work to evaluate f(g(

last: graph your two functions on a coordinate plane. include a table of values for each function. graph the line y = x on the same graph.

Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that

Answers: 2

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answered: pinkbutterfly03

Answers can vary.

This is a very open question.

The ones I chose was

$f(x)=\frac{x+1}{4}$

g(x)=4x-1

When I did f(g(x)) I got the expression back.

The graphs are in the attachment.

Step-by-step explanation:

$f(x)=\frac{x+a}{b}$

$y=\frac{x+a}{b}$

To find the inverse we mainly just need to swap and . Afterwards, we will solve for the new .

Let's begin that process.

$x=\frac{y+a}{b}$

Multiply both sides by :

bx=y+a

Subtract on both sides:

bx-a=y

So the inverse of $f(x)=\frac{x+a}{b}$ is $f^{-1}(x)=bx-a$ .

Comparing this to their inverse which is g(x)=cx-d , we see whatever we choose for the value that's what needs to be and whatever we choose for will be the value of .

So that is in general the inverse of $f(x)=\frac{x+a}{b}$ is g(x)=bx-a .

We should get f(g(x))=x and g(f(x))=x if they are indeed inverses.

Let's verify:

f(g(x))

f(bx-a)

$\frac{(bx-a)+a}{b}$

$\frac{bx}{b}$

That verifies f(g(x))=x .

g(f(x))

$g(\frac{x+a}{b})$

$b(\frac{x+a}{b})-a$

(x+a)-a

x+a-a

That verifies g(f(x))=x .

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Part 1:

So let's pick b=c=4 and a=d=1 .

So this means $f(x)=\frac{x+1}{4}$ and g(x)=4x-1 .

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Part 2:

We are asked to show what f(g(x)) simplifies to.

f(g(x))

f(4x-1)

$\frac{(4x-1)+1}{4}$

$\frac{4x-1+1}{4}$

$\frac{4x}{4}$

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Part 3:

f(x)=4x-1 has slope 4 or 4/1 and -intercept -1.

So I will draw a dot at -1 on the -axis.

From there, I will rise 4 and go right 1 and put another dot.

I also rewrite 4/1 as -4/-1 and so from the -intercept I went down 4 and left 1 also and put a dot.

f(x)=4x-1 has been colored purple.

y=x or y=1x+0 has slope 1 and -intercept 0.

So I will draw a dot at 0 on the -axis.

I will then plot another point by using the slope for this line. The slope is 1 or 1/1 so from the -intercept I will got up 1 and right 1 and put another dot.

y=x is in red.

$g(x)=\frac{x+1}{4}$ or $g(x)=\frac{x}{4}+\frac{1}{4}=\frac{1}{4}x+\frac{1}{4}$ has -intercept is 1/4 and slope is 1/4.

Draw a dot at $\frac{1}{4}$ on the -axis.

I then use the slope 1/4 to graph another point by rising up 1 and going over 4 from the -intercept and putting another dot.

I also wrote 1/4 as -1/-4 and went down 1 and left 4 from the -intercept and put another dot.

$g(x)=\frac{x+1}{4}$ is in blue.

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Another way to graph is use a table of points.

$f(x)=\frac{x+1}{4}$

x | y=f(x) | (x,y)

---------------------------------------------

-5 | (-5+1)/4=(-4)/4=-1 | (-5,-1)

0 | (0+1)/4=1/4 | (0,1/4)

3 | (3+1)/4=4/4=1 | (3,1)

We could graph these points for and then form a straight line with them.

g(x)=4x-1

x | y=g(x) | (x,y)

----------------------------------------------

-1 | 4(-1)-1=-4-1=-5 | (-1,-5)

1/4 | 4(1/4)-1=1-1=0 | (1/4,0)

1 | 4(1)-1=4-1=3 | (1,3)

We could graph these points for and then form a straight line with them.

I put these dots in pink on my graph.

Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that

answered: Guest

step-by-step explanation:

answered: Guest

Answer for 2: his profit would be $2.88 explanation: you have to first multiply 72 and 0.12 together to get $8.64 once you do that you know how much money the shopkeeper made from selling the candy bars individually. so you have to do 8.64-5.76=2.88 hope that ; )answer for 3: yeah i’m sorry i have no idea what number 3 is. i’m sorry i couldn’t with that.
I'm going to add u to plsss answer questions 2 n 3