Question

4.

Answer 1

(a)The domain of the function is, $\rm x \geq -c^2 \ x\neq0$

(b)The given function is discontinuous at x=0.

What is the domain and range of a function?

Domain is the set of values for which the given function is defined. Range is the set of all values which the given function can output.

The standard function is;

$\rm f(x)= \frac{\sqrt{x+c^2-c} }{x} , c > 0$

The domain of the given function is found as;

$\rm x+c^2 \geq 0 \ x\neq 0 \\\\ x\geq-c^2 \ x\neq 0$

The domain of the function is,

$\rm x \geq -c^2 \ x\neq0$

To find the function is continuous or not, we have to find the continuity;

$\rm f(x) = \frac{\sqrt{ x+c^2-c}}{x} ,c > 0$

At x= 0 the function is undefined. So that the function is discontinuous at x=0.

Hence, The domain of the function is, $\rm x \geq -c^2 \ x\neq0$ and the function is discontinuous at x=0.

To learn more about domain, refer to the link:

brainly.com/question/20073127

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