Let f(x) = (g(x))/(h(x)), where g and h ...

Let `f(x) = (g(x))/(h(x))`, where g and h are continuous functions on the open interval (a, b). Which of the following statements is true for `a lt x lt b` ?

A

f is continuous at all x for which `x ne 0`

B

f is continuous at all x for which g(x) = 0

C

f is continuous at all x for which `g(x) ne 0`

D

f is continuous at all x for which `h(x) ne 0`

Verified by Experts

The correct Answer is:

D

Similar Questions

Explore conceptually related problems

For function f(x)=(lnx)/(x), which of the following statements are true?

Write the following as interval. {x : x in R, -2 lt x lt 5}

If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is

Discuss the continuity of the function g(x) = [x] + [-x] at integral values of x.

Find f'(x) if f(x)= (sin x)^(sin x) for all 0 lt x lt pi .

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all x, then g''f(x) is equal to

For every pair of continuous functions f,g:[0,1]->R such that max{f(x):x in [0,1]}= max{g(x):x in[0,1]} then which are the correct statements

State True or False, if 'false' write correct statement. The point (-x,-y) lies in the first quadrant where x lt 0, y lt 0 .