Best Answer

If a function has an inverse then it is a bijection between two sets. Each element in the first set is mapped to one, and only one, element of the second set. Therefore, for each element in the second set there is one, and only one, element in the first set. The function and its inverse, both define the relationship between the same pairs of elements.

Q: Why it is valid to say that both a function and its inverse describe the same relationship.?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

Subtracting its additive inverse. (In principle, this is valid for adding positive numbers as well.)

Domain is a set in which the given function is valid and range is the set of all the values the function takes

The logarithm function is the inverse of the exponential function. Take the exponential function (base 10): y = 10x. The inverse of this is x = 10y. The function y = log(x) is used to define this inverse function. First look at y = 10x. Any real value of x will yield a positive real value for y. If x = 0, then y = 1; if x < 0 (negative) then y is between 0 and 1 (it will never equal zero, though). A value of 10-99999 is very close to zero, but not quite there. There are no real values of x which will give a negative y value for y = 10x. Now look at y = log(x) or x = 10y. No matter what real values for y, that we choose, x will always be a positive number, so a negative value of x in y = log(x) is not possible if you are limiting to real numbers. It is possible with complex and imaginary numbers to take a log of a negative number, or to get a negative answer to y = 10x.

When you plot a function with asymptotes, you know that the graph cannot cross the asymptotes, because the function cannot be valid at the asymptote. (Since that is the point of having an asymptotes - it is a "disconnect" where the function is not valid - e.g when dividing by zero or something equally strange would occur). So if you graph is crossing an asymptote at any point, something's gone wrong.

The validity or invalidity of a function are not abstract but depend on its domain and codomain or range. If for any point, A, in the domain there is a unique point, B, in the range such that f(A) = B then the function is valid at A. The validity of a function can change from point to point. For example, f(x) = sqrt(x) is not a function from the set of Real Numbers to the set of Real Numbers because any negative number in the domain is not mapped to any value in the range. This can be corrected either by changing the domain to the set of non-negative Real Numbers or (if you are a more advanced mathematician) change the range to the set of Complex Numbers. Similarly the reciprocal function, f(x) = 1/x is valid everywhere except for x = 0. Or f(x) = tan(x) is valid except for x = 90+k*180 degrees for all integer values of k - so it is not valid at an infinite number of points.

Related questions

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.

Direct proportion, linear, first-order... all of these are valid answers, depending on the particular field you're talking about.

Subtracting its additive inverse. (In principle, this is valid for adding positive numbers as well.)

Intestate.

Domain is a set in which the given function is valid and range is the set of all the values the function takes

Those are both perfectly valid terms, which you would use according to context. You might say, for example, that obesity has a negative correlation to longevity. And in an aqueous solution there is an inverse correlation between hydrogen ions and hydroxide ions.

The logarithm function is the inverse of the exponential function. Take the exponential function (base 10): y = 10x. The inverse of this is x = 10y. The function y = log(x) is used to define this inverse function. First look at y = 10x. Any real value of x will yield a positive real value for y. If x = 0, then y = 1; if x < 0 (negative) then y is between 0 and 1 (it will never equal zero, though). A value of 10-99999 is very close to zero, but not quite there. There are no real values of x which will give a negative y value for y = 10x. Now look at y = log(x) or x = 10y. No matter what real values for y, that we choose, x will always be a positive number, so a negative value of x in y = log(x) is not possible if you are limiting to real numbers. It is possible with complex and imaginary numbers to take a log of a negative number, or to get a negative answer to y = 10x.

Goal Seek is not a function or an analysis tool. It is a tool that is used to establish a value to be used for a formula. What If and the IF function can be used for analysis. The NOW function is a function but it is not an analysis tool.

The domain of a function is the set of numbers that can be valid inputs into the function. Expressed another way, it is the set of numbers along the x-axis that have a corresponding solution on the y axis.

providing valid information to the decision maker and also for analysis function

When you plot a function with asymptotes, you know that the graph cannot cross the asymptotes, because the function cannot be valid at the asymptote. (Since that is the point of having an asymptotes - it is a "disconnect" where the function is not valid - e.g when dividing by zero or something equally strange would occur). So if you graph is crossing an asymptote at any point, something's gone wrong.

There is no requirement for any statement in a C++ function, let alone three sets of statements. For instance, the following is a perfectly valid function: void foo(){} Clearly this does nothing as it has no statements in the function body, but it is nevertheless a valid function. Perhaps you mean something else by "statements". The only requirement of a function is that it have a return type, a valid name, an argument list and a function body. The return type may be void, of course, and the argument list may be empty, but it must include the ellipses. The function declaration need not include the function body, and the argument list need only specify the type of argument (the argument names are optional and need not match those declared in the actual definition). The function name and the arguments define the function signature (the prototype), thus the three required "components" of a function are the return type, the signature and the function body.