[" 7.If "f(x)=(1+x^(2))],[" 8.If "y=f(x)=(3x+1)/(5x-3)" ,prove that "x=f(y)]

If y= f(x) =(3x-1)/(5x-3) , prove that f(y) =x.

If y= f(x)=(2x+3)/(5x-2) , prove that f(y)=x.

If f(x)=(2x+1)/(3x-2)=y ,show that x=f(y).

(i) If y = f(x) = (3x-1)/(5x-3) , prove that f(y) = x (ii) If y = f(x) = (ax -b)/(bx-a) , prove that f(y) = x

If f(x)=2x^(2)+3x-5 , then prove that f'(0)+3f'(-1)=0

If f(x)= x^5+x^3-2x+3 ,Prove that f'(1)+f'(-1)=4f(0).

If f(x)= 2x^2+3x+5 , then prove that f'(0)+3f'(-1)=0

If f(x)=5^x , then prove : f(x+y)=f(x).f(y)

For a function f(x),f(0)=0 and f'(x)=(1)/(1+x^(2)), prove that f(x)+f(y)=f((x+y)/(1-xy))

If f(x) =x+1/x , prove that : [f(x)]^3 = f(x^3)+3f (1/x) .