Which of the following is an Extreme Value of the function f(c,y) = 2'+y4 4ry - + 1Lutfen birini secin: (0,1)b. (-1,0)c (1,-1)d. (-1,-1)e. (-~1,1)f. (1,0)g. (0...

Find the indicated function values for each function. $$f(x)=\left\{\begin{array}{ll}{x,} & {\text { if } x<0} \\{2 x+1,} & {\text { if } x \geq 0}\end{array}\right.$$ a) $f(-5)$ b) $f(0)$ c) $f(10)$

This problem deals with evaluating a function, given certain values and a little bit of a trick, because their function is given in the form of a constant F of X is equal to seven. So two different ways you go about evaluating this one way is to think of Well, if we're substituting in for X, how many exes are there in this function? Well, I could rewrite this as f of X is equal to zero X. There are no exes, plus seven. And then you can go in and substitute and you'll see that your answer is gonna equal seven each time. So if I go zero times 10 plus seven zero times negative 10 plus seven and zero time zero plus seven zero times anything is equal to zero. So those air all zeros add seven. We get 77 and seven. So it doesn't matter what your input value is, what you're substituting in, it will always equal seven on day. One way you can see that is on a graph, so f of X equal seven would be a horizontal line at the Y axis going through the Y axis at seven. So it doesn't matter what you input for X 123123 Negative one negative to negative. Three negative. 10,000 Negative a million. It will always equal seven. That line will be going at the point of output of seven.

The following problem we want to determine on which of the following intervals is ffx not continuous. So we're going to start off with an example of one over squared backs which it's not going to be continuous. If we look from zero to infinity it will be continuous there. If we look at zero itself when we have it set equal to zero, we see that that is going to be undefined. So they're, the function would not be continuous From 0 to 2 would be continuous. 12, it's continuous and want to infinity it's continuous. Um So it's just going to be when we include the value of zero that it will not be continuous Then if we consider the square root of X -1. Mhm. We see that um there's going to be um we want to know which of the following is not a point of discontinuity. So we see that because one is the least value can be um zero will be discontinuity. Any negative values will be discontinuous, however X equals one will not be a point of discontinuity.

So in this question, they're asking for the range of the function. When you see sign Cheese Square Close Co sign XI squared, this is a fag immune identity. It's equal to science where G plus co sign square Gee, that's always equal toe one. Therefore, the range of the function is always one which is choice no matter what you put in.

We are probably number 238 question says oh that it affects be a continuous function defined X. For expert and zero satisfying affects why equal graphics plus xy F Y affects Y equal to affects place F. Y. And given that after this one equal to one. And so our best 10 willing to find out after 10 we have to find out. So this is definitely in the form of log it affects. Is gay log ex willing to find the value of care for this will be using this condition. So for that we have differentiated after six will be equal to K by X. So after this one will be equal to keep by one. Okay, so this one is one okay, equal to one. So it does play in here will be getting the value of function affects equal to okay, log X. That is log x. So after cash then will be equal to one by 10. That is 0.1. 0.1 should be answered mm An option number B is the correct choice. Thank you.