Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [algebra-precalculus]

For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

This tag is for questions typically taught in precalculus, as well as elementary algebra.

These topics include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomials, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

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What is the value of $f(1999)$?

Let be a function $f \colon \Bbb R\to \Bbb R$ given from: $$f(x)=x^3+\sqrt{x^6+1}+\frac{1}{x^3-\sqrt{x^6+1}}$$ What is the value of $f(1999)$? To me, it immediately seemed strange that it was necessary to calculate $f(1999)$. With a calculator…
Sebastiano
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how does this translate to a circle with radius 5: $\sqrt{24-2x-x^2}$

I tried squaring both sides to get this $y^2 = 24-2x-x^2$, then putting the $x$'s with the $y$'s to get $y^2 + x^2 + 2x = 24$. Then I tried dividing everything by 24, but I don't see it. Tried factoring too.
J L
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What maths is being used to calculate this interest?

I'm curious about how my bank is calculating the interest on my credit card. No matter what I do, I cannot make the numbers add up! Below is a photo of my latest statement. It's for 13th June - 12th July. There were no purchases, but an opening…
Danny Tuppeny
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Solve the equation $(x+1)^4=2(1+x^4)$

Solve the equation $$(x+1)^4=2(1+x^4)$$ The most intuitive approach for me was to use the formula $$(a+1)^4=a^4+4a^3+6a^2+4a+1,$$ so our equation is $$x^4+4x^3+6x^2+4x+1-2-2x^4=0\\-x^4+4x^3+6x^2+4x-1=0$$ $\pm1$ aren't solutions, so this equation…
kormoran
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Rationalize the denominator of $\frac{1}{1+\sqrt[3]{3}-\sqrt[3]{9}}$

Rationalize the denominator of $$\dfrac{1}{1+\sqrt[3]{3}-\sqrt[3]{9}}$$ Usually we are supposed to use one of the formulas $$x^3\pm y^3=(x\pm y)(x^2\mp xy+y^2)$$ I don't think they will work here. We can say $\sqrt[3]{3}=t\Rightarrow t^3=3$ and the…
Math Student
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What is the number of real solutions of the following? $ \sqrt{x + 3 - 4\sqrt{x-1}} + \sqrt{x + 8 - 6\sqrt{x-1}} = 1 $

What is the number of real solutions of the following? $$ \sqrt{x + 3 - 4\sqrt{x-1}} + \sqrt{x + 8 - 6\sqrt{x-1}} = 1 $$ My solution: $$ \sqrt{x + 3 - 4\sqrt{x-1}} + \sqrt{x + 8 - 6\sqrt{x-1}} = 1 $$ $$ \implies \sqrt{(\sqrt{x-1}-2)^2} +…
Parth Thakkar
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If $x = 0$, then $x/x$ is undefined, right?

It's been a while since I worked with math, but I stumbled upon a rather 'simple' equation and the ways of solving it had me thinking for a bit. Consider this equation: $$x(1-x) = x(2 - \sqrt{1-x})$$ Any normal person would consider making the…
Viktor Krum
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Given $a^4+8b=4(a^3-1)-16\sqrt 3$ and $b^4+8a=4(b^3-1)+16\sqrt 3$, find $a^4+b^4$

Given $a^4+8b=4(a^3-1)-16\sqrt 3$ and $b^4+8a=4(b^3-1)+16\sqrt 3$, find $a^4+b^4$ I tried adding and subtracting both equations, but didn't get anywhere. Would appreciated any ideas. Thanks!
user526427
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equation to linear function

I'm doing homework and I've been given a line as the equation $7x-6y=5.$ I need to make a function $y = f(x)$ of this that corresponds to the equation. What I know at this point is that I need to know what the $a$ and $b$ are in $y = ax + b.$ I also…
user1534664
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Bill calculation (very simple math question)

I hope this question isn't too simple! If it is, let me know if I should post it elsewhere, thank you. (Also, I didn't know what to tag it with, sorry!) My wife and I live with my brother-in-law Bob, and, for 30% of the time, also live with Bob's…
Adam George
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A point $(x,y)$ moves so that its distance from the line...

A point $(x,y)$ moves so that its distance from the line $x=5$ is twice as great as its distance from the line $y=8$. Find an equation of the path of the point. I got the two equations: $$x-2y+11=0 \tag{1}$$ $$x+2y-21=0 \tag{2}$$ The book claims…
Jesse
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What conditions hold $f\left(f^{-1}(x)\right)=x$

What conditions hold $f\left(f^{-1}(x)\right)=x$ For example $$\begin{align*}\text{sin(arcsin(x))=x}\end{align*}$$ I think this is a trival question maybe asked too many times, where are they?
HyperGroups
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Overthinking equality of real numbers

This is a very basic question that's been bugging me for some time. I know "=" means equality: that is, the expression on other side of the equation is the same exact number, so doing anything to one side requires the same thing to the other side.…
beginner
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Some (potentially) really simple algebra I can't figure out

Okay so, I couldn't be more specific in the title because honestly I can't make it fit in a way that makes sense. We've been told that: $$A + B = C + D \tag{1}$$ and $$ik_1A - ik_1B = ik_2C-ik_2D \tag{2}$$ I'm trying to show that: $$\frac{A+B}{A-B}…
Panic
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Reformulate $x/(x+y)$ using a single $x$ and $y$

Is it possible to reformulate this expression to only list $x$ and $y$ once using common math functions? The ranges of $x$ and $y$ are both $0$ to $1$ inclusive if that helps. Common being those typically found on a scientific calculator.
Chris
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