24_DETAILSPREVIOUS ANSWERSSCALC8 6.6.507.XPFind f(x) if f'(x) 5/V1 - x2 and f(2) 9 f(x)Need Help?Read [email protected] Tutor...

(4.8) For each function, $f,$ find $f(3)$ and $f(-2)$ $$f(x)=\frac{3}{2} x+5 . \text { Find } x \text { so that } f(x)=\frac{11}{2}$$

We need to find the difference quotient. So we're first gonna replace X with X plus H. So we have to over X plus H minus two minus The original function which is to over explain -2. All over H. So we need to multiply to get a common denominators we're gonna multiply by X plus h minus two on this side, An X -2 on this side. So we end up with two X -4. Then over here we get minus two x minus two. H plus four over our common denominator which is X plus H minus two Times X -2. Fall over age. Yeah so our two exits cancel out our force cancel out and we're left with negative two H divided by X plus h minus two times x minus two divided by one divided by age. So this becomes -2. H over X plus H minus two times x minus two. We change our division to multiplication and we flip are fractions which one over h r h is canceled out and were left as a final answer of -2 over X plus H minus two times X minus two.

Okay, So for this problem, we were given the function of X equals execute loss. We're X and we're told that for a we have negative too. You were asked not only to find what half of a equals, but to also find out whether a is a root of our function of f of X. So our first determination of doing that is just to find out what f of a equals and then to determine whether a is a rude or not FAA equals zero, then a is a route for our function. And if a breath of a is not zero than a is not a root of our functions, so let's just get right to it. I'm putting in minus two for A We have, uh, minus two cubed plus four times minus two and just simplifying. We have minus two times minus two is positive for four times minus two is on minus eight and then we have another minus eight, and that gives us a minus 16. Um, last time I checked minus 16 is not the same as zero. So a is not a route

So we want to find X. We know the H of X is 19. So this goes here. This is 19 now we can solve for X, so you need to subtract seven from both sides. 12 is equal to negative three X, then divided by negative three to both sides, so X will equal to negative for.

Really given problem, we want to consider F of two F and F of one F one over half. Knowing that F of X People's two X Cube. So f of two f. Um It's going to be, well if you consider to F that's going to be um four X Cube. So if we have f of two f, we're going to plug this in here, giving us two times for X cube cube. It ends up giving us um for cube, which is uh 64 so 64 times two is 1 28 1, 28 X two the ninth. That's the graph that we end up getting here, which is the same as this one. So you see that's how we do that. And then if we have F of one over F, we would just divide, put one over this and then compose the functions.