What's the general rule for when applying f(x) = x^2 introduces a "extraneous solution" to a equation?
42803
When do we get extraneous roots?
20568
Does the following have a solution for f(x,y)?
49453
Why do I have to solve for $x$ in this proof, if I choose not to find a counterexample?
146881
Error/warning when using NSolve for simple equation
155655
Applying MVT and IVT (?) to show something about f'''? (edit: actually, Taylor's Theorem using Lagrange remainder)
117338
Counterexample to second derivative test when f''(x) is not continuously differentiable
57411
Manipulating only the denominator in the solution of a fourth order equation
69187
What's my confusion with the chain rule? (Differentiating $x^x$)
52706
Can Reduce *really* not solve for x here?
24862
Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$
58083
what can I say about the solution $y(x)$ of the ODE?
48039
How to solve this ode $xy''-(1+x)y'+y=x^2$?
82206
Solving an equation involving an integral
49211
Solving $f(x+y) = f(x)f(y)f(xy)$
144859
Finding parameters for $f(x) = x^2 + 2(m − a)x + 3am −2 = 0$ that satisfy a condition.
133485
How to solve $\int_0^{\infty} \frac{\log(x+\frac{1}{x})}{1+x^2}dx$?
23465
When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?