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.
| 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 \(g(x) = \sqrt{3x + 15}\) 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 \(g(x) = 3x\). |
| 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… |