document.write( "Question 260299: Hi, I need to find and simplify the difference quotient for f(x + h)- f(x), over h. Where f(x) = 3x + 7. The answer in the book is 3, where h cannot = 0. So I plug in 3x + 7 for every f(x), how do I solve this problem and why wouldn't the (3x + 7) and the -(3x + 7) cancel each other out? Thanks for your help, much appreciated. \n" ); document.write( "

Algebra.Com's Answer #191724 by drk(1908) $\"\"$ $\"About$

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First, we have f(x) = 3x + 7.
\n" ); document.write( "second, We need to find f(x+h).
\n" ); document.write( "f(x+h) = 3(x+h) + 7 = 3x + 3h + 7
\n" ); document.write( "--
\n" ); document.write( "Now we can find $\"%28f%28x%2Bh%29+-f%28h%29%29%2Fh\"$ as
\n" ); document.write( " $\"%28f%28x%2Bh%29+-f%28h%29%29%2Fh\"$ = $\"%28%283x%2B3h%2B7%29-%283x%2B7%29%29%2Fh\"$
\n" ); document.write( "notice what happens in the numerator . . . the 3x + 7 will drop out. This will always happen. We get
\n" ); document.write( " $\"%28f%28x%2Bh%29+-f%28h%29%29%2Fh\"$ = 3h/h
\n" ); document.write( "Now, h approaches 0, so we end with
\n" ); document.write( " $\"%28f%28x%2Bh%29+-f%28h%29%29%2Fh\"$ = 3.
\n" ); document.write( "-- \n" ); document.write( "

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