What Is The Domain Of A Logarithmic Function

Examples on how to find the domain of logarithmic functions with solutions example 1 find the domain of function f defined by f x log 3 x 1 solution to example 1 f x can take real values if the argument of log 3 x 1 which is x 1 is positive.

What is the domain of a logarithmic function. For example in the logarithmic function. Remember that logarithmic functions and exponential functions are inverse functions so as expected the domain of an exponential is such that x r but the range will be greater than 0. However its range is such that y r. What is the domain of the function.

That is the argument of the logarithmic function must be greater than zero. Graphing a horizontal shift of latex f left x right mathrm log b left x right latex. Which points lie on the graph of f x log9x. How can you use a point on the graph of f 1 x 9x to determine a point on the graph of f x log9x.

When finding the domain of a logarithmic function therefore it is important to remember that the domain consists only of positive real numbers. As we mentioned in the beginning of the section transformations of logarithmic functions behave similar to those of other parent functions. We can shift stretch compress and reflect the parent function latex y mathrm log b left x right latex without loss of shape. When determining domain it is more convenient to determine where the function would not exist.

Hence the condition on the argument x 1 0 solve the above inequality for x to obtain the domain. Check all that apply. B f 1 x 9x. Domain is already explained for all the above logarithmic functions with the base 10.

X 1 or in interval form 1. This relationship is true for any function and its inverse. The graph of y logax is symmetrical to the graph of y ax with respect to the line y x. The function is defined for only positive real numbers.

Y log 10 x instead of base 10 if there is some other base the domain will remain same. The graph is nothing but the graph y log x translated 3 units down. What is the inverse of the logarithmic function f x log9x. Switch the x and y coordinates.

Stack exchange network consists of 176 q a communities including stack overflow the largest most trusted online community for developers to learn share their knowledge and build their careers. Graph the function on a coordinate plane remember that when no base is shown the base is understood to be 10. X 0 all real numbers. What is the range of the function.

For example we can only take the logarithm of values greater than 0. For example consider latex f left x right mathrm log 4 left 2x 3 right latex.