0 like 0 dislike
0 like 0 dislike
Taking a radical of 0 and getting not-fully-understood wrong answer

4 Answers

0 like 0 dislike
0 like 0 dislike
You actually get |(x-1)|>=0.

Meaning x-1 >= 0 or 1-x >=0 so x >=1 or  1 >= x.

The square root of x^2 is |x|, not just x
0 like 0 dislike
0 like 0 dislike
(-4)^2 > 0

Take the square root of both sides:

-4 > 0

You have to be more careful than that.
0 like 0 dislike
0 like 0 dislike
not every operation that you can do to an equation will also work if you do it to an inequality, for example taking the square root. functions that preserve inequalities (i.e. functions f where f(x) > f(y) implies x > y) are called increasing functions, and there is no reason to believe that an arbitrary function that you encounter will be increasing. some functions are, like f(x)=x^(3) and f(x)=log(x), but most are not, like f(x)=x^(2) (unless you restrict the domain to the positive reals, in which case it is).
0 like 0 dislike
0 like 0 dislike
In addition to what others have pointed out, an equation like \[f(x)\]\^2 >= 0 is true for all x, since the square of any real number is non-negative.

So as soon as you get to the form (x - 1)\^2 >= 0, you know the solution set is all real numbers.
by

Related questions

0 like 0 dislike
0 like 0 dislike
3 answers
RashidAbdalla asked Jun 21
[The article](https://www.reddit.com/r/statistics/comments/vh2ecs/analysis_of_russian_vaccine_results_suggests_they/) [Twitter summary](https://twitter.com/K_Sheldrick/st...
RashidAbdalla asked Jun 21
0 like 0 dislike
0 like 0 dislike
1 answer
MSR_Tlse asked Jun 21
Are the S3/S4 Edexcel Further Maths units useful to become an actuary? Topics include sampling, unbiased and biased estimators, confidence intervals and significance test...
MSR_Tlse asked Jun 21
0 like 0 dislike
0 like 0 dislike
20 answers
balkissoon asked Jun 21
Considering leaving the actuarial profession. What are some interesting fields you've heard of former actuaries going into? How did they get into the new field?
balkissoon asked Jun 21
0 like 0 dislike
0 like 0 dislike
9 answers
HilaryKHarper asked Jun 21
Has anyone successfully guessed on like half of the questions on an exam and still passed?
HilaryKHarper asked Jun 21
0 like 0 dislike
0 like 0 dislike
0 answers
RyanWCTV asked Jun 21
Range of two Discrete Random Variables
RyanWCTV asked Jun 21

24.8k questions

103k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!