Question

The function f(x)= 3/4x is one-to-one. Find f^-1(x).

Answer 1

That's looking for the inverse of the function. What do you need to do to find an inverse?

Answer 2

I set x= 3/4 * y and then solved for y and got x / (3/4)...then I multiply x but the reciprocal and get.... is it 4/3x?

Answer 3

Should be the same as what you started with.

Answer 4

To find the inverse, all you have to do is switch the places of the y and x :) , first we have the following:

y = 3/4x

the inverse is:

x = 3/4y

then solve ^_^

Answer 5

correct me if I'm wrong :)

Answer 6

You're totally correct.

Answer 7

^_^ remidia, did you understand it?

Answer 8

Did you guys see my second post? Haha I solved it the way you said sstarica and I got (4/3)x as my inverse

Answer 9

hmm, I think I forgot abt switching the numbers too , but atleas you've got it :)

Answer 10

So we have x=3/4y if we multiply both sides by y we get xy=3/4 then divide by x to isolate y and we get y=3/4x as the inverse, which is the same as we started with.

Answer 11

how did she get 4/3? lol I think it should be the same but the positions of the x and y must change, right?

Answer 12

I'm not sure where remidia got 4/3 from. Some algebra mistake. Not all functions have an inverse, and not all inverses switch values.

Answer 13

Beginning equation: y = (3/4)x ----> inverse: x = (3/4)y -----> x/ (3/4) = y -----> multiply by reciprocal (x/1) * (4/3) = y ------> gives me (4/3)x = y
Make sense how I got it now

Answer 14

Yes, but it's not x=(3/4)y the way you had it written; it's x=(3/4y) which makes a difference. So your way is right if the original function is y=(3/4)x but if it's how you wrote it y=3/4x I take that to be y=(3/4x). So either way you have an answer and understand the process. I guess just try to clarify better. In math, it's very important how you write things. No worries though :)

Answer 15

Beginning equation: y = (3/4)x ----> inverse: x = (3/4)y -----> x/ (3/4) = y -----> multiply by reciprocal (x/1) * (4/3) = y ------> gives me (4/3)x = y
Make sense how I got it now

Answer 16

it makes sense to me too I guess lol :)

Answer 17

Like I said, y=(3/4)x has an inverse of y=(4/3)x which is what you have. :) It was just confusing on how you initially wrote the problem.