if f(x)=(1/9)(9x^) what is 3?

Question

I need the answer for this equation

Comments

What is the missing exponent? What does 3 refer to: is it f(3) or x=3, for example?

Answer 1

 

f(x) = 9x + 1 

let y = f(x) 

you get y = 9x + 1 

let y = x and x = y 

you get x = 9y + 1 

solve for y to get y = (x-1)/9 

that's your inverse function. 

if it is a true inverse function, it will be a reflection of the original function about the line y = x. 

to show that, then graph the functions y = x, y = 9x+1, y = (x-1)/9. 

that graph is shown below: 

 

you can pretty much eyeball it and see that the graph of y = (x-1)/9 is a reflection of y = 9x+1 about the line y = x. 

a more exact interpretation is that f(x,y) in the normal equation should be equal to f(y,x) in the inverse equation. 

how you find that out is as follows: 

let x = 5 in the normal equation. 

then you get y = 9x + 1 which becomes 46 

in your normal equation, when x = 5, then y = 46 

in your inverse equation, when x = 46, you should get y = 5. 

the y in the normal equation becomes the x in the inverse equation. 

the x in the normal equation becomes the y in the inverse equation. 

when x = 46, y = (x-1)/9 becomes y = (46-1)/9 becomes y = 45/9 becomes 5. 

f(x,y) = f(5,46) in your normal equation. 

f(y,x) = f(46,5) in your inverse equation. 

this proves they are inverse equations. 

the inverse equation undoes what the normal equation does. 

normal equation takes 5 and makes it 46. 

inverse equation takes 46 and makes it 5.