If f(x) = x+3/3 , then what is f^–1(x) ?

Question

If f(x) = x+3/3  , then what is f^–1(x) ?

myininaya · Answer

is that (x+3)/3 or x+3/3 ?

myininaya · Answer

I bet you mean (x+3)/3

anonymous · Answer

It's supposed to be a fraction, x+3 over 3

myininaya · Answer

So this function you have is linear and therefore 1 to 1.
Which means it has an inverse.
To find the inverse first I will ask you to solve the following for x
$$y=\frac{x+3}{3}$$

myininaya · Answer

You want to get x by itself.

anonymous · Answer

Would I divide the 3 on top with the 3 on bottom to get the x by itself?

myininaya · Answer

No...
You want to undo the division by 3 
So you need to multiply both sides by what?

anonymous · Answer

1/3?

myininaya · Answer

No. 

If we multiply by 3
then 
wouldn't that 3 cancel with the 3 on bottom?

myininaya · Answer

But if you multiply 3 on one side, you must do it to the other

anonymous · Answer

wouldn't that make it x+9/9 ?

myininaya · Answer

Look it is being divided by 3
$$y=\frac{x+3}{3}$$
(see the 3 on bottom that means it is being divided by that 3)
To undo division by 3 we multiply by 3 like so:
$$3 \cdot y=\frac{x+3}{3} \cdot 3 $$

myininaya · Answer

Now what happens if you have 3/3?

anonymous · Answer

it's a 1?

myininaya · Answer

Right! 3/3=1 since 1*3=3
So we have
$$3y=x+3 $$
Now you can finish solving for x?

anonymous · Answer

x=3y-3?

myininaya · Answer

right!
now replace x with f^(-1)(x) and y with x

anonymous · Answer

So the answer ends up being f^(-1)(x)=3x-3?

myininaya · Answer

yes

anonymous · Answer

yayyy thank you for the help :)

myininaya · Answer

np :)

myininaya · Answer

thanks for your hard work! :)