just 2. I got the rest down but these ones are driving me insane.

Find inverse of functions

1. h(x) = 2x/(x+10)

2. f(x) = x^2 + 6x + 11

Thanks.

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- Jan 14th 2007, 06:10 PMFreaky-PersonFunctions and Inverses
just 2. I got the rest down but these ones are driving me insane.

Find inverse of functions

1. h(x) = 2x/(x+10)

2. f(x) = x^2 + 6x + 11

Thanks. - Jan 14th 2007, 07:09 PMThePerfectHacker
$\displaystyle y=\frac{2x}{x+10}$

Substitute x for y and solve,

$\displaystyle x=\frac{2y}{y+10}$

$\displaystyle x(y+10)=2y$

$\displaystyle xy+10x=2y$

$\displaystyle 2y-xy=10x$

$\displaystyle y(2-x)=10x$

$\displaystyle y=\frac{10x}{2-x}$

Quote:

2. f(x) = x^2 + 6x + 11

Horizontal line test, a parabola can be passes twice or more with a horizontal line. - Jan 14th 2007, 07:49 PMFreaky-PersonQuote:

It has no inverse.

Horizontal line test, a parabola can be passes twice or more with a horizontal line.

Like the inverse of y = X^2 is y = +-sqrtX, it's still an inverse even if it's not a function.... - Jan 14th 2007, 07:52 PMAfterShock
- Jan 14th 2007, 08:04 PMAfterShock
- Jan 14th 2007, 08:07 PMFreaky-Person
- Jan 14th 2007, 08:56 PMCaptainBlack
Put:

$\displaystyle y=x^2+6x+11$

then:

$\displaystyle x^2+6x+11-y=0$,

Now use the quadratic formula to get:

$\displaystyle x=\frac{-6 \pm \sqrt{36-4(11-y)}}{2}$

or:

$\displaystyle g(y)=\frac{-6 \pm \sqrt{36-4(11-y)}}{2}$.

Which is not a function when you are looking for functions from

R to R as it fails to be single valued, but it is what you are expected to

produce, and there are interpretations under which it is a function

(such as the extension of f and g to mappings from P(R) the set of

subsets of R, to itself) .

RonL - Jan 15th 2007, 06:21 AMThePerfectHacker
Maybe he is trying to find the inverse,

$\displaystyle f^{-1}: f[\mathbb{R}]\to \mathbb{R}$.

Meaning from the image of the function to the set of real numbers. In that case an inverse exists. - Jan 15th 2007, 02:55 PMFreaky-Person
Kay I got it. I'll post it up for future reference or something like that.

f(x) = x^2 + 6x + 11

y= x^2 + 6x + 11

for inverse

x = y^2 + 6y + 11

x = (y^2 + 6y + 9) + 2

x - 2 = (y + 3)^2

+-sqrt(x - 2) = y + 3

+-sqrt(x - 2) - 3 = y

BTW, anyone know any sort of tutorial for that big letter CODE writing? - Jan 15th 2007, 03:03 PMFreaky-Person
- Jan 15th 2007, 03:50 PMThePerfectHacker
I am impressed, a teenager who actually wants to learn something! I wish more of your types existed, otherwise their philosphy is simple, "If it not on the exam we do not care, we do not need it".

http://www.mathhelpforum.com/math-he...-tutorial.html