Examine whether the following functions are even, odd or neither.i) f(x)= 3x2+cosx+1ii)xsinx+ cosx iii) 10x-10-x

Log_2aa=x    then, a=(2a)^x  ......(1)

Log_3a2a=y    then,2a=(3a)^y ......(2)

Log_4a 3a=z  then, 3a=(4a)^z ......(3)

So, 

a=(2a)^x  [from (1)]

Or, a=(3a)^xy    [from(2)]

Or, a=(4a)^xyz     [from(3)]

Multiplying both sides by 4a,

4a.a=4a.(4a)^xyz  

Or,(2a)² =(4a)^{xyz + 1} 

Or,(3a)^2y =(4a)^xyz+1 

Or,(4a)^2yz =(4a)^xyz+1 

Or, 2yz = xyz+1 .proved.

Here, f: A—>B

f(x)= (x-1)/(x+2)  ;  x   -2 

A= {-1,0,1,2,3,4}

B= {-2,1,-1/2,0,1/2,1/4,2/5}

Range = {-2,-1/2,0,1/4,1/2,2/5}

As range is not equal to codomain so the given function is not bijective. 

We can make it bijective by omitting {1} from set B