As we know,
For a function f(x),
Domain: The values that can be put in the function to obtain a real value. For example: f(x) = x, now we can put any value in place of x and we will get a real value. Hence, domain of this function will be Real Numbers.
Range: The values that we obtain of the function after putting the value from domain. For Example: f(x) = x + 1, now if we put x = 0, f(x) = 1. This 1 is a value of Range that we obtained.
Since, f(x) is defined for x Є R, the domain of f is R.
It can be observed that the range of f(x) = -|x| is all real numbers except positive real numbers. Because will will always get a negative number when we put a value from domain.
Thus, the range of function is f(x) is (-∞, 0].
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