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. ƒ(x)=1-x

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 four minus X. Now, here we are, we have four different answer your choices. A B C and D each with a different solution for the three solutions that we need to find. So beginning with our function F of X is equal to four minus X. We want to begin by 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 four minus X, we now have four minus the quantity of X plus H. Now just simplifying, we see that F of X plus H gives us four minus X minus H. So we have found F of X plus H so we can move on to finding F of X plus H minus F of X. Well, to find the solution to this expression here, we just need to take our solution for F of X plus H and then subtract F of X from F of X plus H. So we have F of X plus H as four minus X minus H and now we subtract the expression of F of X. So we subtract the quantity of four minus X. Now distributing the negative, we have four minus X minus H minus four plus X. Now we just need to simplify this expression by combining our like terms. And we see that F of X plus H minus F of X gives us or simplifies to just negative H. And lastly, we need to find the quant of F of X plus H minus F of X divided by H. And so to solve this expression, we just need to insert or substitute in our value or expression from F of X plus H minus F of X and then divide that expression by age. So we found our numerator expression to just be negative H from our previous solution. So now we will just have negative H divided by age and simplifying, we see that the quantity of F of X plus H minus F of X divided by H Just simplifies to negative one. So with this, we have found our three different solutions for our three different expressions from our problem statement. So with these three solutions, we are left here with answer choice A where F of X plus H is equal to four minus X minus H F of X plus H minus F of X gives us negative H. And finally, the quantity of F of X plus H minus F of X divided by H is equal to negative one. 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. ƒ(x)=1-x

Key Concepts

Function Notation and Evaluation

Difference of Function Values

Difference Quotient

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