0
votes
1answer
14 views

How do I find and list compositions for (f) and (g)?

Ok, I've literally just spent the last 2 hours just to figure out two compositions problems for homework, and I've about had it. Anyone here that can help? Problem 1 $$ f(x) = 2x(2) - x -3 $$ $$ ...
0
votes
1answer
40 views

On the existence/applications of infinitely-nested functions

Inside a previous question, one particular nested function shown is the known tetration. This "kind" of arbitrary repeated functions has always intrigued me, because inside their properties lie so ...
3
votes
2answers
52 views

Composition of functions is constant in $\mathbb{R^2}$.

Let $\hspace{0.05cm}f:\mathbb{R^2}\to\mathbb{R^2}$ $\hspace{0.05cm}$ and $\hspace{0.05cm}$$g:\mathbb{R^2}\to\mathbb{R^2}$ $\hspace{0.05cm}$ be such that$\hspace{0.05cm}$ $g\circ f$$\hspace{0.05cm}$ ...
2
votes
0answers
38 views

Rendering the derivative of composite functions from a graph

I'm on a workbook problem and I want to make sure I'm doing it properly. The problem asks me to find the derivatives of composite functions when given only the graphs of the original functions, here ...
0
votes
1answer
36 views

Composition of functions.

If $h(x) = 2x + 1$, find $h(x + 2)$ ...and a second question. Given $f(x)=x^2+1, g(x)=x-2$, then what is the domain of $f(g(x))$ $\begin{align}\text{Work: } f(g(x)) & =(x-2)^2+1 \\ & ...
2
votes
0answers
55 views

Don't know when to add negative numbers

I'm definitely not a math person and only did general mathematics in high school, and unfortunately, not paying as much attention to that as I should have. Well, I'm doing Discrete Mathematics in my ...
0
votes
6answers
2k views

Application of Composition of Functions: Real world examples?

Do you know of a real world example where you'd combine two functions into a composite function? I see this topic in Algebra 2 textbooks, but rarely see actual applications of it. It's usually plug ...
1
vote
1answer
44 views

Composition of a piecewise and non-piecewise function

Say you have 2 functions, one of which being a piecewise function: $f(x)= x^2+2, x<1$ or $2x^2+2, x>=1$ And the other: $g(x)=x^4+1$ How would you find the $f[g(x))]$? I understand regular ...
1
vote
2answers
107 views

Maximal domain for composite functions.

Question $\mathbf 5$ If $f:(-\infty,1)\to R$, $f(x)=2\log_{\,e}(1-x)$ and $g:[-1,\infty)\to R$, $g(x)=3\sqrt{x+1}$, then the maximal domain of the function $f+g$ is ...
0
votes
2answers
852 views

Find Domain and Range of Composite Function

Given $$f(x) = \{(-5,0),(-4,-2),(-2,3),(1,5),(4,2)\}$$ $$g(x) = \{(0,-2),(8,4),(-2,5),(5,-5),(3,1)\}$$ $1$) Find the domain and range of $f(g(x))$. $2$) Find the domain and range of $g(f(x)$.
1
vote
1answer
45 views

How do i find the values of these functions?

Suppose $f$ and $g$ are one-to-one functions such that $f(2)=7$, $f(4)=2$, and $g(2)=5$. If possible, find the values of A) $(g \circ f^{-1})(7)$ B) $(f \circ g^{-1})(5)$ C) $(f^{-1} \circ ...
0
votes
1answer
43 views

How do I solve this function and find its domain?

Suppose that $f(x)= -x^2+1$ and $g(x)= \sqrt{x}$. How do we find $f \circ g$ and $g \circ f$ and their domains?
1
vote
2answers
76 views

Finding inverse of functions[methods of]

I am now trying to understand functions, inverses and composites. I must admit am not getting a thing. But following some leads, I managed to work one as below. Is this a good understanding on hows ...
0
votes
2answers
176 views

If $f(x) = \frac{x}{\sqrt{x^2 + 1}}$, what is $\underbrace{f(f(f( \dots f}_{2013}(x) \dots )))$?

Given the function $$f(x) = \frac{x}{\sqrt{x^2 + 1}},$$ I need to evaluate the iterated (nested) function $$\underbrace{f(f(f( \dots f}_{2013}(x) \dots ))).$$ I believe the alternative notation ...
3
votes
1answer
41 views

Simple Composisitons

I just need someone to check my work before I go on as I am just checking to make sure I am doing it right. $$g(t) = 2t^2 - 2t ,\ \ \ h(t) = 3t -1$$ $$g(2t^2 - 2t)$$ $$h(g(t)) = 3(2t^2 - 2t) - 1$$ ...
5
votes
1answer
220 views

Sum of terms in a composition cycle

Let $f, g$ be linear functions. Define $S(x)$ as $any$ composition sequence of $f$ and $g$ like $S(x) = (f\circ g\circ g\circ f\circ f\circ g)(x)$ Let $s$ as the fixed point of $S$ then a cycle is ...
0
votes
3answers
85 views

Function Composition Trouble

I'm trying to find $f \circ g \circ h$ when $f(x) = -1/(10x), g(x) = -5x^3$ and $h(x) = -4x^2+10$. The way I did it... $$f(g(h(x)))= f(g(-4x^2+10))$$ $f(-5x^3(-4x^2-10)$ <--- this part confused ...