Question

If f(x) =a(x-b) divided by a-b +b(x-a)divided by b-a then show that f(a) +f(b) = f(a+b)​

Answer 1

Step-by-step explanation:

given

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

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

=> f(a) = a ............(1)

=> f(b) = a( b-b) /( a-b)+b(b-a) ,/ (b-a)

=> f(b) = b.............(2)

=> (1) + (2)

=> f(a )+ f(b) = a+b ...............(3)

f(a+b) = a{ (a+b) - b} /( a-b) + b{ ( a+b) - a} / (b-a)

= a²/(a-b) -b²/(a-b)

= (a²-b²) / (a-b)

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

f(a+b) = a+b ...................,.........(4)

from eqn (3) and (4)

f(a) + f(b) = f( a+b). = a+b

Proved