Question

If f(x)=\(\frac{x+3}{x^2-5x+6}\)  and g(x)=\(\frac{x-3}{x^2-6x+8}\), then which of the following is correct?

(a) f(x) is continuous at x=2 and g(x) is continuous at x=2

(b) f(x) is discontinuous at x=3 and g(x) is discontinuous at x=2

(c) f(x) is continuous at x=4 and g(x) is discontinuous at x=4

(d) f(x) is discontinuous at x=3 and g(x) is continuous at x=2

The question was posed to me at a job interview.

Query is from Continuity in section Complex Function Theory of Engineering Mathematics

Answer 1

The correct choice is (b) f(x) is discontinuous at x=3 and g(x) is discontinuous at x=2

The explanation is: The denominator of f(x) is (x^2-5x=6). When we factorize this, we get, (x^2-5x+6)=x^2-2x-3x+6

(x^2-5x+6)=(x-2)(x-3)

Since the denominator becomes 0 at x=2 and x=3, f(x) is discontinuous at x=2 and x=3.

The denominator of g(x) is (x^2-6x+8). When we factorize this, we get,

(x^2-6x+8)=x^2-2x-4x+8

(x^2-6x+8)=(x-2)(x-4)

Since the denominator becomes 0 at x=2 and x=4, f(x) is discontinuous at x=2 and x=4.