Question

If f(x)=\(\frac{x+3}{x^2-5x}\)and g(x)=\(\frac{x-3}{x^2-6x}\), then which of the following is correct?

(a) f(x) is continuous at x=1 and g(x) is continuous at x=0

(b) f(x) is discontinuous at x=6 and g(x) is discontinuous at x=5

(c) f(x) is continuous at x=5 and g(x) is discontinuous at x=0

(d) f(x) is discontinuous at x=5 and g(x) is continuous at x=5

I had been asked this question in semester exam.

The question is from Continuity topic in chapter Complex Function Theory of Engineering Mathematics

Answer 1

Right option is (b) f(x) is discontinuous at x=6 and g(x) is discontinuous at x=5

Explanation: The denominator of f(x) is (x^2-5x). When we factorize this, we get,

 (x^2-5x)=x(x-5)

Since the denominator becomes 0 at x=0 and x=5, f(x) is discontinuous at x=0 and x=5.

The denominator of g(x) is (x^2-6x). When we factorize this, we get,

(x^2-6x+8)=x(x-6)

Since the denominator becomes 0 at x=0 and x=6, f(x) is discontinuous at x=0 and x=6.