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 | Let $h(x)=4 x+1$. Find $(h \circ h)(x)$ $(h \circ… | \( (h \circ h)(x) = h(h(x)) \) |
| None | \[ \begin{array}{l} s(x)=2 x+1 \\ t(x)=-2 x^{2}+1… | First, we need to find the value of \(s(4)\) by substituting \(x = 4\) into the function \(s(x) = 2… |
| None | Use the pair of functions to find $f(g(x))$ and $… | Given the functions \(f(x) = x^{2} + 8\) and \(g(x) = \sqrt{x + 4}\), we are asked to find \(f(g(x)… |
| None | Let $f(x)=-5 x-1, h(x)=-x+3$ Find $(f \circ h)(-7… | Find the value of h(-7) by substituting -7 into the function h(x) = -x + 3. This gives us h(-7) = 1… |
| None | For $f(x)=9 x-2$ and $g(x)=\frac{x+2}{9}$, find t… | First, we find the composition of the functions $f$ and $g$, denoted as $(f \circ g)(x)$, which mea… |
| None | Use $f(x)=5 x-3$ and $g(x)=2-x^{2}$ to evaluate t… | Given the functions $f(x)=5x-3$ and $g(x)=2-x^{2}$, we are asked to evaluate the expressions $(f \c… |
| None | The functions $u$ and $w$ are defined as follows.… | Define the functions \(u(x) = -x - 1\) and \(w(x) = x^2 + 2\) |
| None | Given the functions below, find $(h \cdot g)(4)$.… | Find the value of the functions $h$ and $g$ at $x=4$. |
| None | Given $f(x)=3 x^{2}-5 \quad$ and $(f \circ g)(x)=… | We are given the function \(f(x)=3 x^{2}-5\) and \((f \circ g)(x)=1-3 x\), and we are asked to find… |
| None | Question 4 Given: $g(n)=n^{3}+5 n$ and $h(n)=3 n+… | Given the functions $g(n)=n^{3}+5 n$ and $h(n)=3 n+3$, we are asked to find the value of $h(g(n+1))… |
| None | Question 3 Given: $f(x)=x^{2}-1$ and $g(x)=x-5$ F… | The question is asking for the composition of two functions, $f$ and $g$, evaluated at $4b$. The co… |