# Tagged Questions

42 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}$ ...
21 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 ...
792 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 ...
89 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 ...
84 views

### function composition - n times

Please consider this function: $$f(x) = \frac{x}{{\sqrt[6]{{1 + {x^6}}}}}$$ What would be the value of the composition (n times): $$f \circ f... \circ f = ?$$ I tried doing it manually, maybe ...
27 views

### Finding a formula using two other functions.

I am trying to find a formula for $p(x)$, but I am not seeing where to start. I have two functions $m(x)=9*27^x$ and $n(x)=9^x$ I need to find the formula for function $p(x)$ if $m(x) = p(n(x))$ ...
51 views

### The limit of a composite function

I am presented with the following task: "You are given that $k(h) \neq 0$ and $h \neq 0$. If $\lim_{k \to 0} F(k) = L$ and $\lim_{h \to 0} k(h) = 0$, show that $\lim_{h \to 0}F(k(h)) = L$. This is ...
306 views

### Left Inverse: An Analysis on Injectivity

I'm told that $g$ is a left inverse of $f$ if $g\circ f=1_X$. I'm also told that if $f$ has a left inverse, then $f$ must be injective. I'm now asked to prove the converse, namely that if ...
Suppose $F(x)=f(g(x))$ $g(1)=3$ $g'(1)=4$ $f'(1)=6$ $f'(3)=5$ What is $F'(1)$ ?
If $f: \mathbb{R} \to \mathbb{R}$ is continuous, and $\forall x \in \mathbb{R} :\;(f \circ f \circ f)(x) = x$, show that $f(x) = x$. The condition that $f$ is continuous on $\mathbb{R}$ is ...