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Find all real values of $x$ for which $f(x)=0.$$$f(x)=x^{3}-x$$...

Question

Find all real values of $x$ for which $f(x)=0.$$$f(x)=x^{3}-x$$

Find all real values of $x$ for which $f(x)=0.$ $$f(x)=x^{3}-x$$



Answers

Find all real values of $x$ for which $f(x)=0.$ $$f(x)=x^{3}-x$$

Using Property five, we can rewrite the into at the integral from 5 0 to 3 of F of X t ax, plus the integral from 3 to 5 off f of x, the X So this is the integral from 0 to 3 of three d x plus being to go from 3 3 to 5 off x x. So if we take the integral, it's three x from 3 0 to 3, plus X squared, divided by two from three years. Five. Pleasant in numbers. We end up with nine plus 25 over two, minus nine over to which is equal to 17.

This problem wants us to find Apple zero when, uh, of X is equal to X squared minus three acts plus two where we find that we're just going everywhere we see an X, we're gonna replace that with parentheses and then in those pregnancies were gonna put in the value we're looking to play again, trying to play in zero. So zero squared minus three times zero is zero. So, plus to our final answer is just gonna equal to okay, thank you very much.

So this question ask, You'd minus three x wintered, and then we have plus X minus three. So what we're gonna do to factor this is really a factor. First, this left part into X squared Times X minus three Austin. And here we have one ministry. Now we can see our zeroes are gonna cure. One expert equals negative. One of Mac's upholstery. So are zeros. We're gonna be three and then plus or minus a high.

We want to know where this function is not continuous. Fractions are non continuous whenever the nominee er is equal to zero. But there's two possibilities here. Either acts could be zero or X squared, minus one could be zero, and that would make a discontinuous. We know X can be zero. We also know X squared minus one can be zero The ex word minus one factors two X plus one times X minus one X plus one would be when it zero when x is negative. One in X minus 10 when x is positive one. So there are three discontinuities here. Negative one zero in positive one.


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