true
True.
True.
true
The domain and range of the composite function depend on both of the functions that make it up.
The domains of polynomial, cosine, sine and exponential functions all contain the entire real number line. The domain of a rational function does not, since its denominator has zeros, and neither does the domain of a tangent function. (1/2)x = true (8/3)x = true
true
True.
True.
true
The domain and range of the composite function depend on both of the functions that make it up.
true
The base of 1 is not used for exponential functions because it does not produce varied growth rates. An exponential function with a base of 1 would result in a constant value (1), regardless of the exponent, failing to demonstrate the characteristic rapid growth or decay associated with true exponential behavior. Therefore, bases greater than 1 (for growth) or between 0 and 1 (for decay) are required to reflect the dynamic nature of exponential functions.
Yes, superposition theorem holds true in AC circuits as well. You must first convert an AC circuit to the phasor domain and the same rules apply.
true
A function is a mapping between two sets, the domain and the range, such that each element in the domain is mapped to only one element in the range. This is true for all lines in a plane except those that are parallel to the y-axis. Thus, all non-perpendicular lines are functions but vertical lines are not functions.
A function is a mapping between two sets, the domain and the range, such that each element in the domain is mapped to only one element in the range. This is true for all lines in a plane except those that are parallel to the y-axis. Thus, all non-perpendicular lines are functions but vertical lines are not functions.