True
false
A positive real number is any natural, integer, rational, or irrational number x such that x>0. In other words, the real numbers indicated by with or without positive sign (+) is known as Positive Real Number. Positive Real numbers are indicated by R+ mathematically.For example R+ = {1, 2, 3, 4, 5, .....}
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!)
If what you mean is F(x) = 63x then the range is all 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.
A radian is simply a measurement unit. The relation between a radian and real numbers is similar to the relation between a degree and real numbers or a metre and real numbers.
True
The range of y = nx consists of all positive real numbers, and the domain consists of all real numbers.
Real numbers include positive and negative numbers, integers and fractional numbers, and even irrational numbers - numbers that are between rational numbers, but that are not rational numbers themselves. (A rational number is one that can be written as a fraction, with integers in the numerator and the denominator.) Real numbers can be represented as points on a straight line.
the domain is all real numbers and the range is all real numbers the domain is all real numbers and the range is all real numbers
Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.
false
Real numbers are all positive numbers except zero.
No.
No, the range of a quadratic function is not all real numbers. A quadratic function, typically in the form ( f(x) = ax^2 + bx + c ), has a parabolic shape. If the coefficient ( a ) is positive, the range is all real numbers greater than or equal to the minimum point (the vertex), while if ( a ) is negative, the range is all real numbers less than or equal to the maximum point. Thus, the range is limited to values above or below a certain point, depending on the direction of the parabola.