Class Eleven Maths

2 Answers

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

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

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

Log_4a3a=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.