Suppose we have 2 + f(x) - [f(x)]^2 that is continuous at point 0. Illustrate...

[AlexSendler100%]

Anybody can help me with this task i dont exactly understand how to approach questions where you need to give example like this?

 

[stapel]

Anybody can help me with this task i dont exactly understand how to approach questions where you need to give example like this?View attachment 36452

When they ask you to give an example, they are suggesting that there is more than one "right" answer. You are being given the option to invent anything you like, as long as it fits the given rules.

 

[Dr.Peterson]

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You need to find some value of b (other than 1 -- do you see why?) that will work.

You want the function [imath]g(x)=2+f(x)-f(x)^2[/imath] to be continuous at [imath]x=0[/imath].

What will [imath]\displaystyle\lim_{x\to0}g(x)[/imath] be?

What must be true of [imath]f(0)[/imath] in order for [imath]g(x)[/imath] to have the appropriate value?

 

[pka]

As written the question is meaningless.[imath] f(x) = \left\{ \begin{gathered} 1\quad x \ne 0 \\ b\quad = 0 \\ \end{gathered} \right.[/imath]
Even it were
[imath] f(x) = \left\{ \begin{gathered} 1\quad x \ne 0 \\ b\quad x = 0 \\ \end{gathered} \right.[/imath] then we need to know [imath]b==?[/imath]
If [imath]b=1[/imath] it is continuous,