6.If `f(x) =(b(x-a))/(b-a) + (a(x-b))/(a-b)` prove that
`f(a+b) =f(a)+f(b)`

If f(x)=(x-a)^2(x-b)^2 , find f(a+b)

If f(x) = y = (ax - b)/(cx - a) , then prove that f(y) = x.

If f(a,b) =(f(b)-f(a))/(b-a) and f(a,b,c)=(f(b,c)-f(a,b))/(c-a) prove that f(a,b,c)=|{:(f(a),f(b),f(c)),(1,1,1),(a,b,c):}|-:|{:(1,1,1),(a,b,c),(a^(2),b^(2),c^(2)):}| .

If y=f(x)=(ax-b)/(bx-a) , the prove that : x=f(y)

If f(x) is a polynomial of degree at least two with integral co-efficients then the remainder when it is divided by(x-a) (x-b) is , where a ne b (1) x[(f(a)-f(b))/(b-a)] + (af(b) -bf(a))/(a-b) (2) x[(f(a) -f(b))/(a-b)] + (af(b) -bf(a))/(a-b) (3) x[(f(b) -f(a))/(a-b)] + (af(b) -bf(a))/(a-b) (4) x [ (f(b) -f(a))/(a-b)] + (bf(a) -af(a))/(a-b)

If f(x)=log_e((1-x)/(1+x)); prove that f(a)+f(b)=f((a+b)/(1+a b))

If y=f(x)=(a x-b)/(b x-a) , show that x=f(y)dot

If f(x)=(x-1)/(x+1) , then prove that: (f(b)-f(a))/(1+f(b)*f(a))=(b-a)/(1+ab)

Let f: RvecR ,f(x)=(x-a)/((x-b)(x-c)),b > cdot If f is onto, then prove that a in (b , c)dot

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