what is the domain of the following?

Question

a. f(x)=7
b. f(x)=(x+1)/(x^2-25)
c. f(x)=square root of x

Answer 1

a. You can plug any number in for x, so the domain is all real numbers.
b. Here you can't make the denominator 0 (undefined), so it would be all real numbers except -5 and +5.
c. Here you can't take the square root of a negative number (unless you go into imaginary numbers), so the domain is all non-negative real numbers (x >= 0)

Answer 2

Keep in mind that the domain of any function consists of all real numbers that can legally be used as input values. For instance, if an input value results in division by zero or taking the square root of a negative number, these operation are not "legal".

For instance, the function of x is defined by,
f(x) = 2/(x+2)

This function allows any value for x except when x = -2 since you cannot divide by zero,

f(-2) = 2/(-2+2) = 2/0 {illegal division operation}

Therefore the domain of the above function is the set of all real numbers, R, except negative 2.

For your functions,
f(x)=7
the domain is the set of all real numbers, R. Two ways to look at this. One way is to say, "no matter what value you enter for x, you will end up with the result of 7." The other way to look at this is through a graph on the x, y axis. This function could be rewritten to look like this,
y=7
This graph looks like a horizontal line at all values of y being 7, where all the x values can be anything (all real numbers, negative, postive and zero), thus the domain is all real numbers, written like this
x = R

For the function,
f(x)=(x+1)/(x^2-25)
Here, the only values that cannot be inserted for x is 5 and negative 5, since you end up dividing by zero again. Thus the domain is the set of all real numbers except 5.
x = R
x ≠ 5
x ≠ -5

For the function,
f(x)=square root of x
the domain can be any real number greater than or equal to zero, expressed as,
x >=0
The above reads as "x is greater than or equal to zero".
Granted, the physicists and electrical sciences use imaginary numbers in their mathematics, which is what you get if you try to take the sqaure root of a negative number.

Hope this helps a little.

Answer 3

The domain is the possible x values that yield an output to the function(x) (or at least a real output)

(a) f(x) = 7 for all x So the domain is R or -inf < x < inf

(b) f(x) = (x+1)/(x^2-25) if x is either 5 or -5 f(x) is undefined (divide by 0) so
our domain is R \ {{5}U{-5}} or x in R x != 5,-5 or

-inf < x < -5 U -5 < x < 5 U 5 < x < inf

(c) f(x) = sqrt(x) is defined for all non-negative x

So our domain is x => 0

Answer 4

a) R
b) x # +5, -5
c) x >= 0

Answer 5

a. domain and range= all real numbers
b. domain = all real numbers except 25
range = all real number except 0
c. domain = all nonnegative real numbers
range = positive and negative real num,bers

Answer 6

PEOPLE, DO YOUR OWN BLOODY HOMEWORK!

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