g(x) = 4x - 20 / 5

Question

find the inverse.

Answer 1

 

Hi Aishantynea -- the inverse function simply "goes backwards" ... verbally: "multiply by five, add 20, divide total by 4" => g^-1 = (5x +20)/4 ... g "maps" 10=> 4, g^-1 maps 4=> 10

Answer 2

Excellent work by Justin L.

 

You can always check your solution with Wolfram Alpha http://www.wolframalpha.com/

 

I already entered this particular problem which I hope was (4x-20)/5  not  4x-20/5 = 4x-4  into Wolfram Alpha's free-form input field   http://www.wolframalpha.com/input/?i=inverse+of+(4x+-+20)+%2f+5

yielding (5x+20)/4 = 5(x+4)/4

 

Wolfram Alpha conveniently plots the initial equation and it's inverse and the Identity or y=x   (y=1x + 0)   Which is also another check.  Both equations should be mirror images about the y=x.

 

This will really be more fun when you do this with quadratic equations.

Hint: Get a small mirror (like cosmetic size) and stand it on the y=x line and look at the

 

mirror from an angle ... you will see the reflection ... meaning you can trace the inverse 

 

You can check your answer algebraically (in addition to the above graphical method) by computing the composite function.  if your original function is f(x) = (4x-10)/5 and your inverse is g(x)=5x+20)/4   then

y = f(g(x) = g(f(x) = x   the Identity y=x    

so let f(x) = (4x-20)/5    and g(x) = (5x+20)/4

let us do f(g(x))

which says use f(x) but where you see x substitute the full g(x)

so

f((5x+20)/4)

( 4 [(5x-20)/4] - 20 ) / 5     Note that the expression in  []  is g(x)

Simplify

( [5x-20] - 20 ) / 5

simplify

5x/5

simplify

x

 

Eureka!

 

You can also do this with a graphing calculator.

 

You can also use the graphing calculator software Desmos (runs on computers, notepads, iPads, ...

I set this problem up for you to clearly indicate that these are inverses

http://www.desmos.com/calculator/8iktru4jpk

Selectively turn the visibility of expressions 3, 4, 5 to show that the expressions 3, 4, 5 are equivalent and equal to Identity.

Answer 3

g(x) = 4x-20/5 

im going to explain this as if its in your book as g(x) = 4x-20

                                                                                 5

 

1) g(x) is essentially the same thing as y, so lets make it 

y =  4x-20
          5

 

 

2) turn the x into y, and turn y into x

 

x= 4y-20

       5

 

3) solve for x

 

 

5x = 4y-20

 

5x+20 = 4y

 

5x+20  = y   <-- thats your inverse function

    4

 

it can also be written as g^-1(x) = 5x+20

                                                    4