Maybe possibly a piece-wise function...
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4 sin(6x) cos(6x) is already a function of a single variable. The variable is ' x '.
function is the relationship between independent variable & dependent variable i.e. F:R-R
Inspired could be though of as an integer as it does not have an exponent. d/dx(inspired) = 0 ==== Or, as a variable with the implied exponent 1. Using the power rule. d/dx(inspired 1 - 1) = inspired0 = 1 ====
The range of a function is the interval (or intervals) over which the independent variable is valid, i.e. results in a valid value of the function.
If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.