Question

Given functions f(x) = (x2-4)/(x-2) and g(x) = x + 2, XER. Then which of the following is correct? =(A) f is continuous at x = 2, g is continuous at x = 2
(B) f is continuous at x = 2, g is not continuous at x = 2
(C) f is not continuous at x = 2, f = g is continuous at x = 2
(D) f is not continuous at x = 2, g is not continuous at x = 2​

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Answer 1

$\Large\text{\underline{\underline{Explanation}}}$

The zero of the denominator cannot belong to the domain.

Hence, $\largef(x)$ is not defined at $x=2$. It is discontinuous for the only point.

However, here is a theorem.

$\text{ \cdots\longrightarrow\boxed{\text{Any polynomial functions are continuous.}} }$

Hence, $\largeg(x)$ is continuous at $x=2$.

$\Large\text{\underline{\underline{Final answer}}}$

$\largef(x)$ is discontinuous at $x=2$.

$\largeg(x)$ is continuous at $x=2$.

Hence, option (C) is the correct answer.

Answer 2

QUESTION :

• Given functions f(x) = (x2-4)/(x-2) and g(x) = x + 2, XER. Then which of the following is correct? =(A) f is continuous at x = 2, g is continuous at x = 2
• (B) f is continuous at x = 2, g is not continuous at x = 2
• (C) f is not continuous at x = 2, f = g is continuous at x = 2
• (D) f is not continuous at x = 2, g is not continuous at x = 2

GIVEN :

• f is continuous at x = 2, g is continuous at x = 2

• f is continuous at x = 2, g is not continuous at x = 2

• f is not continuous at x = 2, f = g is continuous at x = 2

• f is not continuous at x = 2, g is not continuous at x = 2

TO FIND :

• which of the following is correct = ?

SOLUTION :

• f (x) = x - 4 / x - 2

• f ( x) = ( x +2 ) ( x - 2 ) / ( x -2)

• f (x) = x + 2

then, we have get the answer :

• f(x) is continuous at x = 2

thus , C option is correct