SOLUTION: Let f be the function defined by {{{f(x)=2x^4+5}}}. Find f(a+h), f(2a-h).

Algebra ->  Rational-functions -> SOLUTION: Let f be the function defined by {{{f(x)=2x^4+5}}}. Find f(a+h), f(2a-h).      Log On


   

Question 183683: Let f be the function defined by f%28x%29=2x%5E4%2B5. Find f(a+h), f(2a-h).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.


f%28x%29=2x%5E4%2B5 Start with the given function.


f%28a%2Bh%29=2%28a%2Bh%29%5E4%2B5 Plug in x=a%2Bh


f%28a%2Bh%29=2%28a%2Bh%29%5E2%28a%2Bh%29%5E2%2B5 Break up %28a%2Bh%29%5E4 to get %28a%2Bh%29%5E2%28a%2Bh%29%5E2


f%28a%2Bh%29=2%28a%5E2%2B2ah%2Bh%5E2%29%28a%5E2%2B2ah%2Bh%5E2%29%2B5 FOIL


Expand


Distribute



f%28a%2Bh%29=2%28a%5E4%2B4a%5E3h%2B6a%5E2h%5E2%2B4ah%5E3%2Bh%5E4%29%2B5 Combine like terms.


f%28a%2Bh%29=2a%5E4%2B8a%5E3h%2B12a%5E2h%5E2%2B8ah%5E3%2B2h%5E4%2B5 Distribute



So the answer is f%28a%2Bh%29=2a%5E4%2B8a%5E3h%2B12a%5E2h%5E2%2B8ah%5E3%2B2h%5E4%2B5