Login or Sign Up

Ask a New Question

State the largest domain of each of the functions

f:x = 1/1-x and g:x = x-1/x
where x is real number
find the composite functions
i)fog
ii)gof^-1

i)fog: The largest domain of fog is (-∞, 1).

ii)gof^-1: The largest domain of gof^-1 is (-1, ∞).

Did you know?

Did you know that in mathematics, the largest domain of a function refers to the set of all real numbers for which the function is defined? In the case of the function f(x) = 1/(1-x), the largest domain is all real numbers except x = 1, since this would result in division by zero. Similarly, for the function g(x) = (x-1)/x, the largest domain is all real numbers except x = 0, as this would also lead to division by zero. Now, let's explore composite functions! The composite function fog refers to the composition of function f with function g. To find fog, we substitute g(x) into f(x), resulting in f(g(x)). We can simplify this by substituting g(x) directly into f(x). For the composite function gof^-1, we need to first find the inverse of f(x), denoted as f^-1(x). Once we have f^-1(x), we substitute it into g(x) to get gof^-1(x). By understanding the largest domain of a function and exploring composite functions, we can solve interesting mathematical problems and deepen our understanding of calculus and algebraic concepts.