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If $f(x) = x^4 + x^2 + 5x$, evaluate $f(5) - f(-5)$.

 Nov 8, 2014

Best Answer 

 #5
avatar+1090 
+5

I understand, I just made a mistake for a minute but corrected myself.

 Nov 8, 2014
 #1
avatar+1090 
0

I'm not certain, but I think you have to subtract 5 - (-5) = 5 + 5 = 10 for the function. Then you replace all of the x's in $${{\mathtt{x}}}^{{\mathtt{4}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{x}}}^{{\mathtt{2}}}$$ + 5x with 10's. Doing that, we have $${{\mathtt{10}}}^{{\mathtt{4}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{10}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}{\mathtt{\,\times\,}}\left({\mathtt{10}}\right)$$. $${{\mathtt{10}}}^{{\mathtt{4}}} = {\mathtt{10\,000}}$$, $${{\mathtt{10}}}^{{\mathtt{2}}} = {\mathtt{100}}$$, 5(10) = 50 . Then we have 10000+100+50 which can be easily added together to get the answer.

 Nov 8, 2014
 #2
avatar+128570 
+5

This says that we want to put 5  into the function and evaluate the result. Then, we want to put -5 into the function and evaluate that result. Then, we want to subtract the second result fom the first.

However, 5 and -5 put into the first two terms give the same result..and subtracting like results = 0....so we can ignore these

And putting 5 into the last term = 25   .....and -5 into the same term = -25

So   25 - (-25) = 25 + 25 = 50

 

 Nov 8, 2014
 #3
avatar+1090 
0

Oh, I should have caught onto that.

 Nov 8, 2014
 #4
avatar+128570 
0

Gotta be careful here, Mathematician...

What you are doing is evaluating  -5^4 and -5^2

But.......what we should be doing is evaluating (-5)^4  and (-5)^2

See the difference??? 

Remember, "x" is like a box that is holding something.....the sign on "x" is outside the box.... 

 

 Nov 8, 2014
 #5
avatar+1090 
+5
Best Answer

I understand, I just made a mistake for a minute but corrected myself.

Mathematician Nov 8, 2014
 #6
avatar+128570 
0

OK....no prob.....

 

 Nov 8, 2014

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