Function Composition

The process of function composition in mathematics involves utilizing the result of one function as the input for another function. Notationally, it is expressed as (g∘f)(x)=g(f(x)), which implies that the function g is composed with f. In other words, it's the act of applying one function to the outcome of a different function.

The problems about Function Composition

Topic	Problem	Solution
None	For $f (x) = \frac{4}{x + 4}$ and $g (x) = \frac{3}{x}$ , …	Given the functions $f (x) = \frac{4}{x + 4}$ and $g (x) = \frac{3}{x}$ , we are asked to find the compositi…
None	Let $f (x) = \frac{1}{x - 2}$ and $g (x) = \frac{2}{x} + 2$ …	Let $f (x) = \frac{1}{x - 2}$ and $g (x) = \frac{2}{x} + 2$ .
None	For the functions $f (x) = \frac{x}{x - 1}$ and $g(x)=…	Given the functions $f (x) = \frac{x}{x - 1}$ and $g (x) = \frac{11}{x}$ , we are asked to find the composit…
None	For the real-valued functions $g(x)=\sqrt{3 x+15}…	Define the functions $g (x) = \sqrt{3 x + 15}$ and $h (x) = x - 1$ .
None	Suppose that the functions $u$ and $w$ are define…	Define the functions $u$ and $w$ as $u (x) = x^{2} + 1$ and $w (x) = \sqrt{x + 6}$ respectively.
None	For the functions $f (x) = \sqrt{x - 1}$ and $g(x)=3 x…	Let's start with the given functions: $f (x) = \sqrt{x - 1}$ and $g (x) = 3 x$ .
None	Suppose $H (x) = (5 - 7 x)^{5}$ . Find two functions $f…	We need to find two functions $f$ and $g$ such that the composition of $f$ and $g$ gives us the fun…
None	For the functions $f (x) = \frac{2}{x + 3}$ and $g(x)=…	Given the functions $f (x) = \frac{2}{x + 3}$ and $g (x) = \frac{13}{x + 3}$ , we are asked to find the co…
None	For the functions $f (x) = \frac{4}{x - 3}$ and $g(x)=…	Given the functions $f (x) = \frac{4}{x - 3}$ and $g (x) = \frac{13}{x}$ , we are asked to find the comp…