Inverse function?

Question

Everyone in homework help has got this one wrong.

Find the inverse of

F(x) = (7/x) - 3

Should start like

y = (7/x) - 3
y - 3 = (7/x) How do you get x alone?????

Answer 1

Its easiest if you think of always doing the same things on both sides of the = sign. So:
y = (7/x) - 3
y + 3 = (7/x) - 3 + 3
y + 3 = (7/x)
would be your first step. Now you can multiply both sides by x (as long as x doesn't equal zero), so:
(y + 3)*x = (7/x)*x
x (y + 3) = 7

Hopefully you can take it from there, but as a hint, doing a division on both sides of the equation is also allowed.

Answer 2

y = (7/x) - 3
y + 3 = (7/x)

Now just take the reciprocal of both sides:
1 / (y+3) = (x/7)

and multiply both sides by 7:

7 / (y+3) = x

So the inverse is:

f^-1(x) = 7 / (x + 3)

The test of an inverse is f^-1(f(x)) = x. See if this works for the above function:
f^-1(f(x)) = f^-1((7/x) - 3) = 7 / ((7/x) - 3 + 3)
= 7 / (7/x) = x
So ist works, and in case you just scrolled to the bottom of this to check the answer:

f^-1(x) = 7 / (x + 3)

Answer 3

Invert both sides:

x/7 = 1/(y-3)

Then x = 7/(y-3)

Another way is this:
Starting with x, the original function says
invert giving 1/x
multiply by 7 giving 7/x
subtract 3.

The inverse function does the inverses of these in the reverse order, thus

add 3 giving x + 3
divide by 7 giving (x + 3)/7
invert giving 7/(x + 3)

Answer 4

y=7/x-3
y+3=7/x (not -3)
x(y+3)=7
x=7/(y+3)

So F^-1(x)=7/(x+3)

Edit: I don't know why you think everyone on the other page got it wrong. I see two correct answers on your problem.

Answer 5

y - 3 = (7/x)

x = 7/(y-3)

Answer 6

you have almost got it! bring x to left hand side and y-3 to the right hand side. you will get the inverse function as x=7/(y-3).