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Is an exponential function one-to-one?
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.
What is the root of the function in the math problem f of x?
f(x) = ...f is the name of the function, and x is the variable. I guess you could say x is the root of the function, because it is what the function relies on.
How do you calculate f times x?
To calculate f times x, you simply multiply the value of f by the value of x. This can be represented as f * x. For example, if f = 5 and x = 10, then f times x would be 5 * 10 = 50. Multiplication is a basic arithmetic operation that involves repeated addition and is essential in various mathematical calculations.
Retreat is to advance as oppose is to?
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Is 0 a polynomial?
A polynomial is a function which can take the form: f(x) = sum(a_n * x^n) where n is a nonnegative integer. 0 is the constant function which can be represented in the form above by taking a_n = 0 for all n.
