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.
$\displaystyle y=\frac{2x}{x+10}$
Substitute x for y and solve,
$\displaystyle x=\frac{2y}{y+10}$
$\displaystyle x(y+10)=2y$
$\displaystyle xy+10x=2y$
$\displaystyle 2y-xy=10x$
$\displaystyle y(2-x)=10x$
$\displaystyle y=\frac{10x}{2-x}$
It has no inverse.2. f(x) = x^2 + 6x + 11
Horizontal line test, a parabola can be passes twice or more with a horizontal line.
I know it stops being a function, but there should still be an inverse right? Cause you can still draw y=x and flip the original perabola along that line to get the shape, even if it's not a function.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....
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
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?
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