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Trying to figure out what went wrong with the way I solved this

So, a linear function is given. It's $g(x) = 10x + 5$

I know that $\frac{g(a+h) - g(a)}{(a+h) - a}$

I came up with $\frac{[10(a+h) +2] - [10a + 5]}{h}$

I then simplified that down and came up with 20, but apparently that's wrong?

What did I do wrong?

Edit: Ah, I forgot to say I'm trying to find the average rate of change of the function between $x = a$ and $x = a + h$.

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1  
Yes, it's wrong. $$\dfrac{(10 (a+h) + 5) - (10 a + 5)}{h} = 10$$ – Robert Israel Sep 23 '12 at 19:19
    
Note $g(a+h)=10(a+h)+5$, not $10(a+h)+2$ as you have. Still, with what you have, your simplification went awry. You should not have obtained "$20$". Try going through it again (with the proper value of $g(a+h)$, of course)... – David Mitra Sep 23 '12 at 19:23
up vote 4 down vote accepted

$\frac{g(a+h)-g(a)}{(a+h)-a}=\frac{10a+10h+5-10a-5}{h}=\frac{10h}{h}=10$ shows that any difference quotient is $10$.

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Figured what I did wrong; didn't distribute a minus sign. Simple error, thanks guy! – Brandt Sep 23 '12 at 19:26

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