Question

Please help me out. I will fan and medal

Answer 1

\[f^-1 (3)\] when \[f(x) = (2x+3)/5\]

Answer 2

There?

Answer 3

When I came here to help you out, you are already out.. :P

Answer 4

Oh, you are here only..

Answer 5

Let f(x) = y..

Answer 6

\[y = \frac{2x+3}{5}\]
Here, this is \(y\) in terms of \(x\),,

can you find \(x\) in terms of \(y\) ?

Answer 7

Im very sorry, my internet is really unstable :(
But in this case, would x = 3 ? Since f^-1(3)?

Answer 8

@eta

Answer 9

What I got out of this is as follows:
y = 2x+3/5
y = 2(3)+3/5
y = 6+3/5
y=9/5
Im not sure if this is right, though

Answer 10

@eta

Answer 11

See, you have to find \(f^{-1}(x)\) first..

Answer 12

Do as I said above..

Answer 13

@eta how would I find that though? I'm not sure how to

Answer 14

you have:
\[y = \frac{2x+3}{5}\]

Answer 15

Multiply by \(5\) both the sides..

Answer 16

What you get?

Answer 17

\[5y = 10x + 15/25 ?\]

Answer 18

Really?

Answer 19

Can't you cancel 5 with denominator 5 on right side?

Answer 20

\[5y = \frac{2x+3}{5} \times 5 \\ 5y = 2x + 3\]
Isn't it?

Answer 21

How can 5 cancel out if it is being multiplied by itself? Sorry, I am really bad at this :(

Answer 22

One 5 is in numerator and other is in denominator, you can cancel it like this:
\[\frac{2x+3}{\cancel{5}} \times \cancel{5} = 2x +3\]

Answer 23

Ah, okay. I see now ^^

Answer 24

What comes next, after \[5y = 2x +3?\]

Answer 25

Now, subtract \(3\) from both the sides and tell me what you got?

Answer 26

\[5y-3 = 2x?\]

Answer 27

Good.. :)
Now divide by \(2\) both the sides..

Answer 28

\[5y-3/2 = x\]

Answer 29

yep.
So:
\[x = \frac{5y-3}{2}\]

Answer 30

Now, switch \(x\) and \(y\) to finally find your inverse.
Replace x with y and y with x in the above equation..

Answer 31

\[y = 5(x)-3/2\]. And x = 3, right?

Answer 32

So, you will get:
\[y = \frac{5x-3}{2}\]

Answer 33

This is your f inverse, replace y here with \(f^{-1}(x)\).
So:
\[f^{-1}(x) = \frac{5x-3}{2}\]

Answer 34

Here, put \(x=3\), yes right..

Answer 35

Okay. So \[f^-1(x) = 12/2?\]

Answer 36

And 12/2 simplifies to 6

Answer 37

There you are..!! Good..

Answer 38

So 6 is the final answer, yes? ^^

Answer 39

Thank you very much ^^

Answer 40

\(\dagger\)