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.

$ƒ (x) = - 4 x + 2$

Accepted Answer

Hey, everyone here we are asked to solve for F of X plus H F of X plus H minus F of X and the quantity of F of X plus H minus F of X divided by H for the following function F of X is equal to negative four X plus seven. So here we have four different answer choice options, different choices for both A B C and D and each of these answer choices have three different solutions of the three solutions we are trying to find. So we can begin with first finding F of X plus H. Well, to find F of X plus H, we just need to substitute in X plus H for X from our original function. So instead of negative four X plus seven, we now have negative four times the quantity of X plus H plus seven. Now we just need to simplify by substituting in or distributing this negative four into our parentheses expression here. So we see that F of X plus H gives us negative four X minus for H plus seven. So now that we have found our first required solution, we can move on to finding the expression F of X plus H minus F of X. Well, to find the solution to this expression, we just need to substitute in our expression that we found for F of X plus H and substitute in the expression for F of X. So starting with F of X plus H again, we have negative four, X minus four H plus seven and now we subtract F of X. So we now have minus the quantity of negative four X plus seven. Now we need to simplify by first distributing the negative sign. So we have negative for X minus four H plus seven plus four, X minus seven. Now simplifying this expression, we see that both of the four X terms cancel out as well as both of the seven terms cancel out. So finally, we see that F of X plus H minus F of X simplifies to negative four H. So now we can move on to finding our third expression where we have the quantity of F of X plus H minus F F of X divided by H. And to find the expression here, we just need to repeat the same process as before where we substitute in the expression that we have, which is F of X plus H minus F of X. And then we take that expression and divided by H. So substituting in our expression, we substitute in negative for H which is now divided by H So now simplifying, we see that both of the H terms cancel out since they are in the numerator and the denominator. So we see that the quantity of F of X plus H minus F of X divided by H gives us just negative four. So now we have found our three required solutions for our problem. So with these three solutions, we are left with answer choice C where F of X plus H is equal to negative four, X minus four H plus seven F of X plus H minus F of X is negative for H. And finally, the quantity of F of X plus H minus F of X divided by H is equal to negative four. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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.
$ƒ (x) = - 4 x + 2$

Key Concepts

Function Notation and Evaluation

Difference of Function Values

Difference Quotient

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