In Matlab Why does the bisection method fail for fx 1x wit

In Matlab : Why does the bisection method fail for f(x) = 1/x with error given by |b a|? Hint: How does f(x)

violate the bisection theorem?

Solution

Bisection theorem: If f(x)is a continuous function on [a,b] and f(a) and f(b) have opposite signs then the equation f(x)=0 has a root in [a,b].

when f(x)=1/x it has opposite signs only in an interval of the form [-a,a] for some positive real number \'a\'.

but f(x)=1/x is not continuous on [-a,a] as it is discontinuous at x=0 and any interval of the form [-a,a] contains zero.

therefore f(x) does not satisfy the necessary conditions of the bisection theorem and hence it fails.