inverse F.BF.4 Find inverse A function and its inverse function can be described as the "DO" and the "UNDO" function functions. functions. A function takes a starting value, performs some operation on this value, a. Solve an equation of and creates an output value. The inverse function takes the output value, performs the form f(x) = c for a some operation on it, and arrives back at the original function's starting value. simple function f that has an inverse and write and If functions f and g are inverse functions then. A function composed with its inverse write an expression for the function yields the original starting value. Think of them as "undoing" one another inverse. and leaving you right where you started. Numerically an inverse is found by simply interchanging the x and y coordinates. This newly formed inverse will be a relation, but may not necessarily be a function. Consider this subtle difference in terminology: Definition: INVERSE OF A FUNCTION: The relation formed when the independent variable is exchanged with the dependent variable in a given relation. (This inverse may NOT be a function.) Definition: INVERSE FUNCTION: If the above mentioned inverse of a function is itself a function, it is then called an inverse function. logarithms F.LE.4 For exponential Logarithms are values of logarithmic functions. A logarithmic function is defined as models, express as a and is the inverse of the exponential function , where and logarithm the solution to a bct = d where a, c, and d Logarithms are the "opposite" of , just as subtraction is the opposite of addition and are numbers and the base division is the opposite of multiplication. Logs "undo" exponentials. Technically b is 2, 10, or e; evaluate speaking, logs are the of exponentials. the logarithm using technology.
inverse function F.BF.4 Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write and write an expression for the inverse. A function and its inverse function can be described as the "DO" and the "UNDO" functions. A function takes a starting value, performs some operation on this value, and creates an output value. The inverse function takes the output value, performs some operation on it, and arrives back at the original function's starting value. If functions f and g are inverse functions then. A function composed with its inverse function yields the original starting value. Think of them as "undoing" one another and leaving you right where you started. Numerically an inverse is found by simply interchanging the x and y coordinates. This newly formed inverse will be a relation, but may not necessarily be a function. Consider this subtle difference in terminology: Definition: INVERSE OF A FUNCTION: The relation formed when the independent variable is exchanged with the dependent variable in a given relation. (This inverse may NOT be a function.) Definition: INVERSE FUNCTION: If the above mentioned inverse of a function is itself a function, it is then called an inverse function. logarithms F.LE.4 For exponential models, express as a logarithm the solution to a bct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Logarithms are values of logarithmic functions. A logarithmic function is defined as and is the inverse of the exponential function , where and Logarithms are the "opposite" of , just as subtraction is the opposite of addition and division is the opposite of multiplication. Logs "undo" exponentials. Technically speaking, logs are the of exponentials.