Quant Concept - Functions Part-II

Continuing to previous post on Functions, here are some more concepts on Functions..

Inverse of a function :
Inverse of a function exist only if, for every value of a dependant variable "y", ther exists only and only one value of independant variable "x".
So when ever question comes to find the inverse of a function, what you have to do is:
Replace every occurance of x with y, for e.g
you are given following function f(x)= 1/(x-2), and you have to find an inverse of this function, now, replace every x with y, so we have x= 1/(y-2)
Make this equation in the form of y,
therefore, y=1+2x/x => 2 + 1/x which is an inverse of the function.

Relationship between y=f(x) & y=f(x)+c
If you have a function of the form y=f(x)+c, then graph of your function will be shifted up on the x-y axix by "C" units.

E.g :
1) y=f(x)-c
Graph will be down by "C" units on x-y axis.

2)y=f(x+c)
Graph will be shifter to the left on x-y axix by "C" units.

3) y=f(x-c)
Graph will be shifted on to the right on x-y axix by "C " units.

Some important points:
For two functions to be identical , their domain should be EQUAL.
Domains of some functions:
1) y= root X => x>=0
2) y= root x => x>=0
3) y= root x^2 => x>=0

Hope this helps to many..
Happy studying..

Regards,
Ameya