Posted by Audrey on Wednesday, July 29, 2009 at 8:47pm.
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
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!
Yes, the calculation is correct.
Note: You may not have noticed that you omitted the division sign in the initial post.
Thanks for pointing that out!
You're welcome!
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