Posted by **Audrey** on Wednesday, July 29, 2009 at 8:47pm.

Which would be the inverse of this:

Let f(x)=(x+3)(2x-5)

f^ (-1) x = (5x - 3)/ (2x + 1)

f^ (-1) x = (5x + 3)/ (2x - 1)

- Algebra -
**MathMate**, Wednesday, July 29, 2009 at 9:29pm
Could you check if there wasn't a typo, namely,

"Let f(x)=(x+3)**/**(2x-5)... "

If that's the case, it's the second response.

To double check,

let g(x)=f^{-1}(x)=(5x+3)/(2x-1)

Evaluate

f(g(x))

= ((5x+3)/(2x-1)+3)/((2(5x+3))/(2x-1)-5)

= x

- Algebra -
**Audrey**, Wednesday, July 29, 2009 at 9:47pm
Let y = f(x)

y = (x + 3)/ (2x - 5)

Switch x and y.

x = (y + 3)/ (2y - 5)

Multiply both sides by (2y - 5).

2xy - 5x = y + 3

Subtract 3 from both sides.

2xy - 5x - 3 = y

Subtract 2xy from both sides.

-5x - 3 = -2xy + y

Factor the right side.

-5x - 3 = y (-2x + 1)

Divide both sides by (-2x + 1).

(-5x - 3)/ (-2x + 1) = y

(5x - 3)/ (2x + 1) = y

Now we replace y with the inverse function notation: f^ (-1) x.

f^ (-1) x = (5x + 3) / (2x - 1)

This my work to reflect the answer. Is it correct? Thanks!

- Algebra -
**MathMate**, Wednesday, July 29, 2009 at 9:57pm
Yes, the calculation is correct.

Note: You may not have noticed that you omitted the division sign in the initial post.

- Algebra -
**Audrey**, Wednesday, July 29, 2009 at 10:08pm
Thanks for pointing that out!

- Algebra -
**MathMate**, Wednesday, July 29, 2009 at 10:19pm
You're welcome!

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