Paragraph Consider the function y = f ( x ) f : R - 0 R The functional rule for the function y=f(x) is same as that of the functional rule for hypotenuse ' h ' of the right triangle with area 25 (units) ^2 expressed as a function of its perimeter. On the basis of above information, answer the following : Question The sum of all the values of x at which fof ( x ) is discontinuous -

Step-by-step solution

aligned & 1 2 a b=25 a b=50 & a+b+h=x & h=x-(a+b) aligned Now, a ^2+ b ^2= h ^2 aligned & (a+b)^2-2 a b=h^2 & (x-h)^2-100=h^2 & x^2-2 x h+h^2-100=h^2 & h= x^2-100 2 x aligned aligned & f( x )= x ^2-100 2 x & f is discontinuous at x =0 & f(f( x ))= f ^2( x )-100 2 f ( x ) aligned aligned & f(f(x)) is discontinuous at all x, & where f(x)=0 & x^2-100 2 x =0 x= 10 aligned Sum of values of x where f(f( x )) is discontinuous is 0+10-10=0 .