Asked by Trevor g
find an expression for F(x) and state the domain of F
when F^-1(x)= 1-5x/2x for 0 < x <= 2
when F^-1(x)= 1-5x/2x for 0 < x <= 2
Answers
Answered by
Reiny
First of all, I will assume you meant:
F^-1(x) = (1-5x)/(2x), or else I would have just reduced to F^-1(x) = 1 - 5/2 = -3/2 , a constant
The inverse of the inverse of a function would be the function, that is,
the inverse of F^-1(x) would be F(x)
so we just need the inverse of y = (1-5x)/(2x)
interchange the x and y's
x = (1-5y)/(2y)
2xy = 1 - 5y
2xy + 5y = 1
y(2x + 5) = 1
y = 1/(2x+5)
<b>F(x) = 1/(2x + 5)</b>
check: let x = 5
F^-1(5) = (1 - 25)/10 = -2.4
F(-2.4) = 1/(-4.8 + 5) = 1/(.2) = 5
It is highly likely that my answer is correct
F^-1(x) = (1-5x)/(2x), or else I would have just reduced to F^-1(x) = 1 - 5/2 = -3/2 , a constant
The inverse of the inverse of a function would be the function, that is,
the inverse of F^-1(x) would be F(x)
so we just need the inverse of y = (1-5x)/(2x)
interchange the x and y's
x = (1-5y)/(2y)
2xy = 1 - 5y
2xy + 5y = 1
y(2x + 5) = 1
y = 1/(2x+5)
<b>F(x) = 1/(2x + 5)</b>
check: let x = 5
F^-1(5) = (1 - 25)/10 = -2.4
F(-2.4) = 1/(-4.8 + 5) = 1/(.2) = 5
It is highly likely that my answer is correct
Answered by
Reiny
Just saw the domain part ... 0 < x ≤ 2
F^-1(0) = undefined, but F^-1(x) ----> negative infinity
F^-1(2) = (1-10)/4 = -9/4
so the domain of F(x) is
- infinity < x < -9/4
F^-1(0) = undefined, but F^-1(x) ----> negative infinity
F^-1(2) = (1-10)/4 = -9/4
so the domain of F(x) is
- infinity < x < -9/4
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.