# Tagged Questions

Elementary questions about functions, notation, properties, and operations such as function composition.

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### What are all the different classes of functions upon real numbers and what do they mean, exactly? [closed]

I have been hearing terms like "piecewise C1", "continuous", "linear", "piecewise constant", "trigonometric", "logarithmic", "exponential", "elementary", etc. functions for many years. I know what ...
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### Prove that $f$ is invertible

Did I show enough to prove $f$ is invertible? Alternatively is there a more efficient way to do so? Thanks in advance for any help. Let $f : X \rightarrow Y$a nd $g : Y \rightarrow X$ be ...
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### If $C\cap D=\emptyset$ Prove that $f^c(C)\cap f^c(D)=\emptyset$

Is this the proper way to go about proving this? By showing $C\cap D$=$f^c(C)\cap f^c(D)=\emptyset$? Any feedback would be greatly appreciated. I don't have any other way of getting feedback for my ...
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### Help with Trigonometric Functions

so while playing around with circles and triangles I found 2-3 limits to calculate the value of $\pi$ using the sin, cos and tan functions, I am not posting the formula for obvious reasons. My ...
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### Is the definite integral $\int\limits_a^b {f(x)dx}$ a function of $f(x)$?

I was wondering if definite integrals are functions of their integrands. For example, if $y=\int\limits_a^b {f(x)dx}$, can we call $y$ a function of $f(x)$ ?
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### How to determine if a function is quasiconcave or quasiconvex using calculus

I would like to know if there is a theorem which links the quasi concavity of a function to the sign of its second order derivative. For eg. we know a function is Concave in a given interval if it's ...
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### Problem in equality of two functions.

First of all, my book states that two functions $f$ and $g$ are equal iff.: $Dom(f) = Dom(g)$ $Codom(f) = Codom(g)$ For each $x\in Dom(f)$ , $f(x) = g(x)$ and vice-versa. which is fairly ...
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### Finding the function of a sine graph that has both translation and transformation

I can't quite find a problem similar enough to this yet, and I need some serious help. Here is a photo of the graph of the function I am trying to find out: Sorry, but I don't have enough ...
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### Simplification of this function

$f(x)= ((1- 4x^2)^{1/2} - 2(3)^{1/2}x)/((3-12x^2)^{1/2} + 2x)$ Find range when $x$ belongs to $(-(3)^1/2 /4 ,1/2)$ I have to find the range of this function , I have simplified this expression , I ...