Question

If f(x) =1/x-1,show that,f(a/b)+f(b/a)=-1​

Answer 1

f(x) = 1/x-1 then

• f(a/b) = 1/a/b-1 (REPLACE X BY a/b )

= 1/a-b/b

= b/a-b

• f(b/a) = 1/b/a-1

= 1/b-a/a

= a/b-a

• f(a/b)+f(b/a) = b/a-b + a/b-a

= b(b-a) + a(a-b)/(a-b)(b-a)

= b^2-ab +a^2-ab / ab-a^2-b2+ab

= a^2+b^2-2ab/ -(a^2+b^2-2ab )

= -1

HENCE WE REQUIRED ANSWER