Question

what is f^-1(4) when f(x)=(3x-4)/5?

Answer 1

@ranga help?

Answer 2

@ParthKohli help?

Answer 3

You need to find the inverse of f(x). To do that follow these steps:
1. Replace f(x) with y.
2. Interchange x and y. That is, put x in the place of y and y in the place of x.
3. Solve for y. This will be the inverse.
4. replace y with f^-1.
5. Find f^-1(4) by putting x = 4 in the inverse function.

Answer 4

so f^-1(4) would = -4?

Answer 5

I m getting a different answer. If you show me the steps I can try to spot any mistakes in the steps.

Answer 6

i dont know how much is f^-1(4)

Answer 7

First you have to find the inverse of the function. I gave you the steps above. What is the inverse function you are getting? f^-1(x) = ?

Answer 8

3y-4/5?

Answer 9

What you have is step #2. x = (3y - 4) / 5.
In step#3, solve for y. That is y = ?

Answer 10

how would i solve for y ?

Answer 11

x = (3y - 4) / 5
To solve for y, isolate y.
multiply both sides by 5.
Add 4 to both sides.
divide both sides by 3.

Answer 12

i cant do it i nee to see step by step :/

Answer 13

x = (3y - 4) / 5
multiply both sides by 5. What do you get?

Answer 14

so it would be x=15y-20?

Answer 15

@ranga

Answer 16

When you multiply the left hand side by 5, x will become 5x.
When you multiply the right hand side by 5, it will cancel out the 5 in the denominator and you will be left with just (3y - 4)

Answer 17

ooh alright got it now whats next? replace y with f^-1 so it'll be 5x=3f^-1-4?

Answer 18

Not yet. You have to solve for y first.
x = (3y - 4) / 5
multiply both sides by 5:
5x = 3y - 4
add 4 to both sides:
5x + 4 = 3y
divide both sides by 3
(5x+4)/3 = y or
y = (5x + 4) / 3
Now do step 4 and replace y with f^-1(x)
f^-1(x) = (5x + 4) / 3
f^-1(4) = ?

Answer 19

-4 @ranga

Answer 20

Then just plug in -4 into the x?

Answer 21

Not -4, plug in +4.

Answer 22

What do you get when you put x = 4 in (5x + 4) / 3 ?

Answer 23

i get 8

Answer 24

Yes.

Answer 25

so thats the answer?

Answer 26

Yes.

Answer 27

thank you @ranga you're the best!

Answer 28

You are welcome. Thanks.