Q: When is a function would be positive real function?

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The absolute value of a number is positive, so the range is always a positive real number. You are correct. The domain, that is the value before you take the absolute value, is all real numbers, but the range is always positive.

An arithmetic function is any function which is defined for all positive integers, and has values which are either real or complex.

Time. Time cannot be negative, only positive.

To start with, when you multiply an even number of negative numbers, the answer is positive. When you multiply an odd number of negative numbers, the answer is negative. When you multiply any number of positive numbers, the answer is always positive. For positive numbers, the value of a power is always positive. For negative numbers, the value of an odd power is negative, and the value of an even power is positive. Finding roots is the inverse of taking powers, so that an odd-root function can be evaluated for any value of x. An even-root function, however, cannot be evaluated when the value of x is negative, since an even power can never result in a negative answer. The domain of an odd root function is all real numbers; the domain of an even root function is the non-negative real numbers.

Discriminant = b2 - 4ac A positive answer means two real roots, a 0 answer means one real root and a negative answer means no real roots. Example X2 + 3X - 10 = 0 a = 1 b = 3 c = -10 32 - 4(1)(- 10) = 49 ----------------a positive answer telling you this quadratic function has two real roots.

Related questions

Domain of the logarithm function is the positive real numbers. Domain of exponential function is the real numbers.

The absolute value of a number is positive, so the range is always a positive real number. You are correct. The domain, that is the value before you take the absolute value, is all real numbers, but the range is always positive.

An arithmetic function is any function which is defined for all positive integers, and has values which are either real or complex.

the range is a positive real number

The logarithmic function is not defined for zero or negative numbers. Logarithms are the inverse of the exponential function for a positive base. Any exponent of a positive base must be positive. So the range of any exponential function is the positive real line. Consequently the domain of the the inverse function - the logarithm - is the positive real line. That is, logarithms are not defined for zero or negative numbers. (Wait until you get to complex analysis, though!)

No, because the inverse function would not work. Every time you multiply a positive by a positive you get a positive.

To start with, when you multiply an even number of negative numbers, the answer is positive. When you multiply an odd number of negative numbers, the answer is negative. When you multiply any number of positive numbers, the answer is always positive. For positive numbers, the value of a power is always positive. For negative numbers, the value of an odd power is negative, and the value of an even power is positive. Finding roots is the inverse of taking powers, so that an odd-root function can be evaluated for any value of x. An even-root function, however, cannot be evaluated when the value of x is negative, since an even power can never result in a negative answer. The domain of an odd root function is all real numbers; the domain of an even root function is the non-negative real numbers.

Because that is the way the tan function is defined!

Time. Time cannot be negative, only positive.

false

Discriminant = b2 - 4ac A positive answer means two real roots, a 0 answer means one real root and a negative answer means no real roots. Example X2 + 3X - 10 = 0 a = 1 b = 3 c = -10 32 - 4(1)(- 10) = 49 ----------------a positive answer telling you this quadratic function has two real roots.

Yes, the domain(input) would be all natural numbers (numbers greater or equal to zero). The range (output) would be all real numbers. -- Not only natural numbers would be considered part of this domain, all negative numbers are also reasonable inputs to this function, as any negative number multiplied by itself would produce a positive number..... The output (range) would therefore be all positive real numbers......