For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)...

Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=x^2+3x+1

Accepted Answer

Offer F of X plus H F of X plus H minus F of X and F of X plus H minus F of X over H for the following function where we have X squared plus five, X plus three. Let's look for F of X plus H first. So everywhere we have an extra gun, instead replace it with X plus H. So we have X plus H squared plus five times X plus H plus three. We can expand this two X squared plus two H X plus H squared. Then we have plus five X plus five H plus three. You can't stop the fire anymore. So that is our F of X plus H. Now, we want F of X plus H minus F of X. The alphabet is H we know is X squared plus two H X plus H squared Plus five, X Plus five, H minus three. Let me subtract X squared plus five, X plus three. We get X squared plus two H X plus eight squared plus five, X plus five, H minus three minus X squared minus five X and minus three. And those are pluses right there. Now. We can cancel that stuff. Here. X squares will cancel out R five, X will cancel out and R 3's will cancel out. Meeting us with two HX plus H squared plus five H which we can factor out an H to get H times two X Plus H Plus five. Now, we want F of X plus H minus F of X over H so just take what we got before H times two X plus H plus five divided by H, we end up with two X plus H plus five. You now have everything we're looking for. Now, if you look at our possible answers, we can determine that the answer to our problem turns out to be answer B which follows every one of the things we calculated. Okay. I hope to help you solve the problem. Thanks for watching. Goodbye.

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For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=x^2+3x+1