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

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.

$ƒ (x) = 1 + 2 x^{2}$

Accepted Answer

For F of X plus H F of X plus H minus F of X and F of X plus H minus F of X divided by H for the following function, our function is four plus three X squared. Now what we can do first is take F of X plus H to do this, we all plug in X plus H for every X in our function. So we get four plus three times X plus H squared. Now, we can expand this. We have four plus three X plus A squared, expands X squared plus two H X plus H squared. Multiplying by three, we get four plus three squared, A six H X Plus 3, 8 square, cancel the fight anymore. So this is our F of X plus H. Now we want F of X plus H minus F of X. What we said F of X plus H is four plus three, X squared plus six H X plus three H squared. Let me subtract four plus three, X squared carrying the negative. We get four plus three, X squared plus six, X plus three, H squared minus four minus three X squared and we can cancel out terms, cancel our fours and our three X squares. We end up with six H X plus three H squared Bachelor on H one B H times six X plus three H. Finally, we want to check our F of X plus H minus F of X over H we have a church, six X plus three H divided by H H is canceled. We get six X plus three H. Now have everything we need for the answer. And if you look at the possible answers, we can determine the answer to. Our problem is the answer is c okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

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.
$ƒ (x) = 1 + 2 x^{2}$

Key Concepts

Function Notation and Evaluation

Difference of Function Values

Difference Quotient

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