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

9 answers
Question:

Write a function that repersents this process:
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

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