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A __________ function takes the exponential function's output and returns the exponential function's input.

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A logarithmic function takes the exponential function's and returns the exponential function's input?

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A logarithmic function takes the exponential function's output and returns the exponential function's?

input


Why are logarithms and exponential functions inverses?

Logarithms and exponential functions are inverses because they effectively "undo" each other. An exponential function, such as (y = b^x), transforms an input (x) into an output (y), while the logarithm, (x = \log_b(y)), takes that output (y) and returns the original input (x). This relationship can be expressed mathematically: if (y = b^x), then (x = \log_b(y)), confirming that one function reverses the effect of the other. Thus, they are defined as inverse operations in mathematics.


Do exponential functions have a domain that includes all real numbers?

Yes, exponential functions have a domain that includes all real numbers. This means that you can input any real number into an exponential function, such as ( f(x) = a^x ), where ( a ) is a positive constant. The output will always be a positive real number, regardless of whether the input is negative, zero, or positive.


What are some characteristics of the graph of an exponential function?

An exponential function is a nonlinear function in the form y=ab^x, where a isn't equal to zero. In a table, consecutive output values have a common ratio. a is the y-intercept of the exponential function and b is the rate of growth/decay.


What is a composite function?

This is a combination of two functions, where you apply the first function and get a result and then fill that answer into the second function. OR These are what you get when you take the output of one function and use it to solve the output of the next function.


What is the function of an output device?

it is the imput of the computers gasilitory functions and after words it is released in the output


In the inverse variation function what happens to the output when the functions input is doubled?

the output is halved


What is function of output devices?

it is the imput of the computers gasilitory functions and after words it is released in the output


What is function of an output device?

it is the imput of the computers gasilitory functions and after words it is released in the output


What is the domain for all exponential growth and decay functions?

The domain for all exponential growth and decay functions is the set of all real numbers, typically expressed as ((-∞, ∞)). This is because exponential functions can take any real number as an input, resulting in a corresponding output that represents either growth or decay, depending on the base of the exponent.


How do you find the functions to a two stage function machine?

To find the functions in a two-stage function machine, start by examining the input-output pairs provided. Identify the first function by determining how the input is transformed into an intermediate output, and then analyze how this intermediate output is further transformed into the final output by the second function. You can express these functions algebraically by using variables to represent the input and output, and solving for the relationships. Testing your functions with various inputs can help verify their accuracy.