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(2 points) Are the following functions analytic? Justify yOur answer.(a) f() =2 (b) f() =e-"(cos(z) + i sin(~) )...

Question

(2 points) Are the following functions analytic? Justify yOur answer.(a) f() =2 (b) f() =e-"(cos(z) + i sin(~) )

(2 points) Are the following functions analytic? Justify yOur answer. (a) f() =2 (b) f() =e-"(cos(z) + i sin(~) )



Answers

Given the following functions, find the indicated values. $$f(x)=\frac{1}{2} x$$ a. $f(0)$ b. $f(2)$ c. $f(-2)$

We happen but 65 in which weapon provided had affects equal to minus five. So there is no variable here. So anyone really off for anyone who's have X effects should be on Li minus five because this it isn't on is a constant function. After Zito, minus five f off 606 this is also minus five. Everything will be called to minus five.

Okay, let's say we're looking at F of X plus two as our equation here. So f of X is equal to X plus two. And we have a Siris of functions we want to find. 1st 1 is f of zero. We also have f of to f of negative five and f of three. A. Last but not least, we have f of A plus one. So what we're gonna do is we're gonna each time substitute what's in the parentheses. This X here for the X over here. So we're taking this ex whatever it is and putting it into our function for the 1st 1 I'm just rewriting what we have, right, which is lips. I don't need to write that part again. We're just gonna put the expose to just emphasize we're doing a substitution on. And then over here will put the number that actually equals. So f of zero would be zero plus two, which gives us two f of two would be two plus two, which gives us four f of negative five instead of X plus. Two will have negative five plus two. The negative and a positive right gives us negative three there f of three A. My seemed tricky, but it's not. We still take the X out and put in whatever is in the parentheses, which is three a. Can we simplify that? Any Ferber? No. So that's going to be three. A plus two for F of three A for F of A plus one instead of X will have a plus one plus two. Now, here we can combine our two and one and we get a plus three.

Okay, let's f of X is equal to X plus two. So that means that for every value of X save, we have ever zero or we have ever tube f of negative five f of three A. And we have f of A plus one. So what we're gonna do is we're gonna substitute in the value of X with the value that is presented here in our target function. Right? So instead of having X here, we would have zero. So then this becomes zero plus two, right, Which is gonna equal to. So we'll put what equals in this column and where we're starting in this common in the middle is just our function, which is X plus two. In this case, um, where each time making a substitution instead of X we're gonna have with what's in our parentheses here. So instead of X plus two, I'll have two plus two, which is four f of negative. Five would be negative five plus two, which would give us negative three and f of three. A. Means will have three a plus to remember those air not like terms, so we cannot actually add them anymore than to rewrite it as three A plus two. They won't combine. They won't change if we have a plus one plus to the two and the one will add together. So then we'll have a plus three. So that would be the extent of our function in this case.

Let's start by finding if evaluated at negative two. That's going to be negative to part three plus two. That's equal to negative. Eight. Still, which is equal to um under your six analysis called that if our function is 1 to 1, which dysfunction is then or function f from we have our investors function is equal to or its domain musical to the range of our original function. So, no, it's not that we have a number of six year, and then it's ranges acquitted. The domain of original function, so we get just here is equal to negative, so


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