I realized about something today

Algebra Level 2

Find all the values of $x$ such that satisfies the equation $x + 1 = x + \frac{x}{x}$

1 0

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\mathbb R - \{0\}

2 solutions

Roman Frago
Mar 20, 2015

I assume that $R-0$ means R such that $x \neq 0$ .

Hjalmar Orellana Soto
Mar 20, 2015

Now, this is what i realized today: If you have an ecuationyou can write it as $f(x) = g(x)$ . So you graph the functions and find the intersection. It's completely the same for most of the ecuations, but when you've got an ecuation with a lot of solutions, like $x + 1 = x + \frac{x}{x}$ , it's helpful.

It works, I do that too sometimes :P But it generally doesn't help when the roots are complex.

Omkar Kulkarni - 6 years, 2 months ago

Yup! It's correct .

Can you do me a favor ? Try plotting the graph of $y = x +\frac{x}{x}$ , or try using this online graphing calculator .

It'll be the same as y= x+1 . So ??

Look , R - {0} is not the Range of this function . Please check it out yourself to convince yourself .

After you have done that , think if your answer to this question is correct or not :)

A Former Brilliant Member - 6 years, 2 months ago

Nope, the graph of $y = x + \frac{x}{x}$ has an empty space at $x = 0$ .33

Hjalmar Orellana Soto - 6 years, 2 months ago

That shouldn't be the case . Can you post a pic here ?

A Former Brilliant Member - 6 years, 2 months ago

@A Former Brilliant Member – I'll let it in the solution

Hjalmar Orellana Soto - 6 years, 2 months ago

I realized about something today

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