Question

write the domain of the following functions:f(x) = 15xf(x)=1/sqrt(x-2)f(x)=1/(x-2)f(x)=sqrt(x)

Answer 1

First, the function:

$f(x)=15x$

is a polynomial function, therefore, its domain is all real numbers.

next, we have the function:

$f(x)=\frac{1}{\sqrt[]{x-2}}$

In this case, the domain must be all values for x where the square root on the denominator is positive, that is:

$x-2>0$

then, we have that the domain of this function is all the real numbers greater than 2.

Now, for the function:

$f(x)=\frac{1}{x-2}$

the only value that would make the function undefined is x=2 ( since we cannot have a 0 in the denominator), then, the domain of the function f(x) is all the real numbers except 2.

Finally, for the function:

$f(x)=\sqrt[]{x}$

We have that the square root is defined only on the positive real numbers, therefore, the domain o this function is all positive real numbers including 0