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Find the following for each function: (a) $f(0)$,(b) $f(1)$,(c) $f(-1)$,(d) $f(-x)$,(e) $-f(x)$,(f) $f(x+1)$,(g) $f(2 x)$,(h) $f(x+h)$.$$f(x)=1- rac{1}{(x+2)^{2}}$$...

Question

Find the following for each function: (a) $f(0)$,(b) $f(1)$,(c) $f(-1)$,(d) $f(-x)$,(e) $-f(x)$,(f) $f(x+1)$,(g) $f(2 x)$,(h) $f(x+h)$.$$f(x)=1- rac{1}{(x+2)^{2}}$$

Find the following for each function: (a) $f(0)$,(b) $f(1)$,(c) $f(-1)$,(d) $f(-x)$,(e) $-f(x)$,(f) $f(x+1)$,(g) $f(2 x)$,(h) $f(x+h)$. $$f(x)=1-\frac{1}{(x+2)^{2}}$$



Answers

For each function defined as follows, find (a) $f(x+h)$ (b) $f(x+h)-f(x)$ , and $(\mathrm{c})[f(x+h)-f(x)] / h .$
$$f(x)=2 x+1$$

A number fifty six of ex People's ninety one over X Square. I want to find a as explosive. H equals just plugging. Experts urge square which ISS ninety one over X squared plus two X h plus H square in the Halifax plus h Miners have ax equals likely one over X were bussed to access H plus H square Barnes while we're at square minus minus Class Action Yes. You see, ah is after that plus h minus f ax over age. So is this part right? While X squared minus what are X squared plus two x h plus square over, then missive. We can simplify that. I think if you want assemble if I's gonna be angst where x squared plus two x square x squared plus two ex age eight square miles square over a tch Just ah subtract so's you can find the common denominator, which is his part. And, uh, sub tribes become pawns. So what do we have here, Chris forthis Kansas and you do it by h so Eve course to ax plus H. U h. Hansel's former ax square explorer of us two ex age positive square that

This is problem 22. Given the functions F of x equals one minus x over X and G of X equals 1/1 plus X square, solve for the following A. We're going to solve for G F F of X. And solving for this we have to substitute and R f of X into our G fx equation which gives us one over one plus the quantity one minus X over x squared. Now we have to simplify so simplifying we get 1/1 plus one over X. Sorry one minus X over X Times one -X over X. And that would simplify to 1/1 plus one minus two. X plus X squared over X squared. And we are going to rearrange our numerator of this portion of the denominators such that X square dispersed following X squared plus bx plus C. So this third line reads one over X squared over X squared plus X squared minus two X plus one over x squared using the least common denominator. And then we simplify that to 1/2, X squared minus two X plus one divided by x squared, adding our enumerators. And that simplifies to X squared over two, X squared minus two X plus one. By multiplying by the reciprocal For part B. We just substitute in two into our equation. Sorry, our answer that we solve for in part A. So by substituting in two, we got to square divided by two times two squared minus two times two plus one and the numerator we have four and in the denominator we have two times four minus four plus one, and that simplifies to four, divided by eight minus four plus one, which simplifies the four steps.

Question were given the function F thanks Go to three X squared minus four X plus one. And there was NASCAR to fight I the f off far. So only to do is we put the vilifying to this X now, and we should get in. Go to jail terms for square minus four times four plus one And then we should get now You called your death 16 times far 16 times three Go to 48 minus 16. Bless one. So I should get me going to 23 in B. We had defined ah fo minus half. So we're gonna have in time again. A three minus. I have square miles four times minus and have plus one. Then we should get a good job. Three and a four on then place. Yeah, to less one. And then we should get in code you three out of four plus three and we put image of the same common denominator that could you fit in and took far in C. Where'd you find that? Ever I So which need to But I injured Xia. Ever have a tree tree? A square now minus four. I bless one in D where defied Ever you are. I am So we're going to replace the expert you over AM Square minus four Teoh am burlesque one on and in a any evil of the excess than effects. But you won so miss not want to find a f X Could you won And if actually go to the three x squared minus four x plus one. So bad aquatic formula. We should have now First week and cancer the one with the one and that isn't implies that no tree X squared minus four. Thanks a coach, Izzo, and we confront that the X outside in some Have a tree x minus for you. Go to zero It isn't implies that x months ago Juzo x months ago, Joe for under three

Thanks. Echo Judah two X plus one and in part A. We need to fight the F up Express lunch on we need to do is what you play this x here by the Express Arch and was getting now June Temps Experts brunch plus one and we can submit finishing you don't get your express two plus one in B major find ever express crunch minus F of X. Therefore, we get Geico Jew. The ever experts lunch will be this one. So him that you expressed you aren't plus one minus a FX will be this one. So we minus two X minus one Big unfunded mandates miners near because manners for everything Now it was unified. We see done that your ex country when it your eggs one with one and then we have left with only two lunch in. See when a fighter ever. Experts lunch when it's f X divided by lunch. So we have the talk exactly included at your lunch here they're very by lunch here we can get to the art of the arch and then we have eventually got to do it. And that's what made the answer


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