00:01
There is a question.
00:02
To say that determine further each of the following relational functions is even odd or neither.
00:08
So let us just get an idea about the conditions for even and odd function.
00:18
If we have a function, y equal to f x, okay, y equal to f x, then condition for the even function, even function.
00:35
Would be let's write an even function would be like of minus x equal to f x then it is even function odd function when f minus x equal to minus fx and if these two conditions are not satisfied then it would be neither even nor odd now let us go to the function one by one in my case i will be writing a f x is 2x cube plus 8 x squared divide by x cube plus 4x squared so f minus x i will replacing x with minus x in given f x 2 minus x cube plus 8 minus x squared divide by minus x q plus 4 to minus x squared minus 2 x q plus 8 x squared divide by minus x q plus 4 x squared and if i take minus 2 common it would be x q minus 4 x squared and a minus 1 common and minus 1 common q plus 4x squared it is going to be equal to 2 okay this is 2 but i need to find solution in terms of fx only so i will be just taking minus common from numerator so it would be minus 2 or simply 2x 2x cube i'm taking minus common from here 2xq minus 8 x squared divided by x q minus minus 4x square x q minus minus 4x square minus minus would get cancelled out so it is 2xq minus 8 x squared and x q minus 4x squared so this is neither equal to fx and xx and not equal to minus f x so it will be neither answer will be neither part b f x is being given as x cubed divided by 7 x squared plus 1 so f minus x is minus x q divide by 7 x squared plus 1 so f minus x q divide by 7 into minus x squared plus 1 so minus x q by 7x squared plus 1 so minus x q by 7 by 7 squared plus 1 and this is fx so minus fx hence this will be an r function okay part c fx is being given as one by x squared plus nine x raise to the power six you can see that we have even powers all around so if we plug in it will be simply fx let us see it's x squared plus nine minus x raise to the power six so 1 by x squared plus 9 x2 power 6, which is equal to fx.
04:48
That means it is going to be equal to an even function.
04:55
Okay, with part d, fx equal to x squared minus 4 by x minus 2.
05:08
So f minus x equal to minus x whole square minus 4 divided by minus x minus 2...