I need help with these two questions. I'm not getting the same answer in the back of the book.
f(x) = (1+x^4)/(x^2)
for which I got (6x^5-2x)/(x^4)
and the answer at the back is (2x^4-3)/(x^3)
And this question I don't get at all.
f(x) = (5-(1/x))/(x-3)
What are we doing here? Differentiation?
first derivative line :
f'(x) = [x^2(4x^3) - 2x(1+x^4)]/x^4
= [4x^5 - 2x - 2x^5]/x^4
= (2x^5 - 2x)/x^5 , now divide each term by x
= (2x^4 - 2)/x^3
looks like both you and the back of the book are wrong!
Let's go through each question step by step and see how to get the answer.
1. For the first question:
f(x) = (1+x^4)/(x^2)
To simplify this expression, you need to divide the numerator by the denominator. Here's how you can do it:
Step 1: Distribute the x^4 term to each term in the numerator:
(1+x^4)/(x^2) = (x^4 + 1)/(x^2)
Step 2: Divide each term in the numerator by the denominator:
(x^4)/(x^2) + 1/(x^2) = x^(4-2) + 1/(x^2) = x^2 + 1/(x^2)
So, the simplified expression is f(x) = x^2 + 1/(x^2).
It seems like you made a mistake while dividing the terms, which is why you got a different answer than the one in the back of the book.
2. For the second question:
f(x) = (5-(1/x))/(x-3)
To simplify this expression, you need to combine the fractions. Here's how you can do it:
Step 1: Find a common denominator for the two fractions. In this case, the common denominator is x:
[(5 * x) - 1] / (x * (x - 3))
Step 2: Distribute the x factor in the numerator:
(5x - 1) / (x * (x - 3))
That's the simplified expression for f(x).
If the back of the book has a different answer, it's possible that they performed some extra simplifications or rearrangements that are not immediately evident. It would be helpful to compare the steps you followed with any given solution or explanation in the book to pinpoint the discrepancy.
I hope this helps! Let me know if you have any further questions.