2
votes
2answers
69 views

Please solve the equality of this function.

Let $f,g,h:\mathbb R\to \mathbb R$. Show that: $$ (f+g)\circ h = f\circ h + g \circ h $$ $$ (f\cdot g)\circ h = (f\circ h)\cdot(g \circ h) $$ I know that $(f+g)(x)=f(x)+g(x)$. But I don't know how ...
0
votes
1answer
46 views

Write the function as a combination of elementary functions

$2xe ^{(-4x^2)}$ Is this correct? $f(x) = -4x^2, g(x) = e^x, h(x) = 2x$ $h(x)\cdot g(f(x))$
1
vote
1answer
51 views

Introduction to Analysis: Properities of Functions

If I remember correction from my abstract algebra course, if $f(x)$ is defined for all x and is bounded, then composition mapping $f\cdot g$ is also bounded, and so should $g\cdot f$ since the range ...
0
votes
1answer
139 views

Composition of Periodic Functions.

Suppose $f(x)$ is defined for all $x$; then $f \circ \cos x$ is periodic and $2 \pi$ is a period. Conversely, if $g(x)$ is defined for all $x$ and is periodic, with $2 \pi$ as a period, can one find a ...
0
votes
3answers
59 views

Composite bounded functions

Prove $f(x)$ is bounded $\rightarrow$ that $f(g(x))$ is bounded. For all x in $f(x)$ ang $g(x)$. To my understanding, suppose $f(x)$ is bounded, then do we need to show that the composition function ...
2
votes
1answer
59 views

Composition of two functions in $\mathbb{Z^2}\to \mathbb{Z^2}$

I need to find the composition of a function and its inverse so I have the identity function in return. My problem is that I don't seem to undestand how to proceed algebraically. I have a function ...
0
votes
3answers
81 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 ...