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Domain means what values x can take for a function f(x) so that it is defined.

And range of functional value that f(x) can take is the range of a function.

For example:

if f(x) = x², then x can take any value. So domain is (-∞,∞)

The values that f(x) can take are all positive numbers and 0. So range is [0,∞)

Another example:

if f(x) = 1/(1-x)

Here x can take any value except 1. x can't take the value 1 as at x=1, function is not defined. So domain is (-∞,1) U (1,∞).

And f(x) can take any value. So range is (-∞,∞)

And range of functional value that f(x) can take is the range of a function.

For example:

if f(x) = x², then x can take any value. So domain is (-∞,∞)

The values that f(x) can take are all positive numbers and 0. So range is [0,∞)

Another example:

if f(x) = 1/(1-x)

Here x can take any value except 1. x can't take the value 1 as at x=1, function is not defined. So domain is (-∞,1) U (1,∞).

And f(x) can take any value. So range is (-∞,∞)