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	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 $f (x) = 5 x - 3$ 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 $f (x) = 3 x^{2} - 5$ 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 $4 b$ . The co…