0
Yes, if you accept that the definition of the exponential function f is given by the two statements (1) f(0)=1, and (2) f'(x)=f(x) for all real x, then you have from differential equations that the function is represented by a power series $f(x)=sum_{k=0}^\infty \frac{x^k}{k!}$. If you accept that this means that f(x) is everywhere positive, then you have that f is monotone (increasing), which implies that it is one-to-one by the mean value theorem.
Add your answer:
Earn +20 pts
A logarithmic function takes the exponential function's and returns the exponential function's input?
output
Is an exponential function is the inverse of a logarithmic function?
No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.
What is the domain of logarithm and exponential function?
Domain of the logarithm function is the positive real numbers. Domain of exponential function is the real numbers.
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.
Can a exponential function be a negative number?
Well -x^3/4 would be exponential
A function takes the exponential function's output and returns the exponential function's input?
A __________ function takes the exponential function's output and returns the exponential function's input.
What is the parent function for the exponential function?
The parent function of the exponential function is ax
Is the inverse of an exponential function the quadratic function?
No. The inverse of an exponential function is a logarithmic function.
A logarithmic function takes the exponential function's and returns the exponential function's input?
output
A logarithmic function takes the exponential function's output and returns the exponential function's?
input
What is a relation which are exponential function?
Exponential relationship!
Is y equals x4 an exponetial function?
If the question is, Is y = x4 an exponential function ? then the answer is no.An exponential function is one where the variable appears as an exponent.So, y = 4x is an exponential function.
How do you change an exponential functions to a logarithmic 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.
Example of fundamental difference between a polynomial function and an exponential function?
fundamental difference between a polynomial function and an exponential function?
Is an exponential function is the inverse of a logarithmic function?
No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.
What is exponential function?
"The" exponential function is ex. A more general exponential function is any function of the form AeBx, for any non-xero constants "A" and "B". Alternately, Any function of the form CDx (for constants "C" and "D") would also be considered an exponential function. You can change from one form to the other.
What is the domain of logarithm and exponential function?
Domain of the logarithm function is the positive real numbers. Domain of exponential function is the real numbers.
