# Write a function that repersents this process: a: take a number, x. b: multiply it by4. c: subtract

###### Question:

a: take a number, x.

b: multiply it by4.

c: subtract 2 from the result

then find the inverse of this function. does the inverse represent the reverse of the process above ? explain why or why not.

## Answers

The function:

Start with x and multiply it by 4

4x

then subtract 2

y=4x-2

To find the inverse, switch x and y and solve for y.

x=4y-2

Add 2 to both sides

x+2=4y

Divide by 4 on both sides

(1/4)x+1/2=y

I don't quite understand what it means by "Does the inverse function represent the reverse of the process" but hopefully the inverse can get you started!

1. [tex]y=\sqrt{x-2}[/tex]

2. [tex]y=x^{2} -3[/tex]

Both will be functions

Step-by-step explanation:

[tex]f(x)=5x-6\\\\y=5x-6\\5x=y+6\\x=\dfrac{y+6}{5}\\\\f^{-1}(x)=\dfrac{x+6}{5}[/tex]

The inverse is a function. In general, the inverse of non-constant linear function, is a function.

Let the function be represented by f(x).

Multiplying the number x by 4 results in 4x. Subtracting 2 from results give 4x - 2. So the function becomes:

f(x) = 4x - 2

Finding the inverse function:

Replace f(x) by y, and isolate x on one side of the equation and find the inverse:

[tex]y = 4x - 2\\\\ y + 2 = 4x\\\\ x = \frac{1}{4}(y + 2)\\ \\ f^{-1}(y)=\frac{1}{4}(y + 2)\\ \\ f^{-1}(x)=\frac{1}{4}(x + 2)[/tex]

Yes the inverse function represents the reverse process. Original function involved multiplication by 4 and then subtraction of 2. Inverse function involves addition of 2 and then division by 4. So the inverse represents the reverse of the given process.

Step-by-step explanation:

firstly suppose f(X) as y and later interchange it with x and solve it to get inverse function of x.

[tex]Find the inverse of the function Find the inverse of the function f(x)=2x-4[/tex]

The two functions are inverses.

Step-by-step explanation:

We are supposed to find whether the two functions are inverses.

[tex]f(x)=5x+4[/tex]

[tex]g(x)=\frac{x-4}{5}[/tex]

To find the inverse of f(x)

y = 5x+4

y-4=5x

[tex]\frac{y-4}{5}=x[/tex]

Replace x with y and y with x

So, [tex]\frac{x-4}{5}=y[/tex]

So, [tex]\frac{x-4}{5}=g(x)[/tex]

So,The two functions are inverses.

A) Find the inverse of the function

s=0.04n+2500

s-2500=0.04n+2500-2500

s-2500=0.04n

s/0.04-2500/0.04=0.04n/0.04

25s-62,500=n

n=25s-62,500

The inverse of the function is n=25s-62,500

Is the inverse a function?

Yes, the inverse is a function, a linear function.

b) Use the inverse to find the same amount of merchandise sold if the employees salary was $2820 last month.

s=2,820→n=25(2,820)-62,500

n=70,500-62,500

n=8,000

The amount of merchandise sold was $8,000

F^-1 (x)= sqrt(5x)/ sqrt(5x), -sqrt(5x)/5 is the inverse of the function y=5x^2

To find the inves

solve for x and replace x with finverse and y with x

y=5x^2+2

minus 2

y-2=5x^2

divide by 5

(y-2)/5=x^2

sqrt both sides

[tex]x= \sqrt{\frac{y-2}{5} }[/tex]

[tex]x= \frac{ \sqrt{ y-2}}{ \sqrt{5} }[/tex]

[tex]x= \frac{ \sqrt{5( y-2)}}{5 }[/tex]

[tex]x= \frac{ \sqrt{5y-10}}{5 }[/tex]

inverse

[tex]f(x)^{-1}= \frac{ \sqrt{5x-10}}{5 }[/tex]

for it to be a function, every x must corespond to exactly 1 y

seems to corespond to 1 each

it is a function