y=2x+bx+a2xy+by=x+ax(2y−1)=a−byx=2y−1a−byf−1(x)=2x−1−bx+a If
f(x)=f−1(x),2x−1−bx+a=2x+bx+a Comparing,
b=−1■ If
a=−21, then
f(x)=2x−1x−21=21 which does not have an inverse as it is not one-one
Hence
a can take any real value except
−21a∈R,a=−21■