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Given f(x)=2x+5,simplify f(x+h)-f(x)/h

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2 Answers

f(x + h)- f(x)/h
 
Given
f(x) = 2x + 5
 
f(x + h) would mean adding h to wherever there's an x.
 
Therefore;
f(x + h) = 2(x + h) + 5
f(x + h) = 2x + 2h + 5
 
Next, we'd solve f(x + h)- f(x)/h
 
= [(2x + 2h + 5) - (2x + 5)] / h
 
= (2x + 2h + 5 - 2x - 5) / h
 
= (2x - 2x + 2h + 5 - 5) / h
 
= (0 + 2h + 0) / h
 
= (2h) / h
 
= 2
f(x+h) = 2(x+h) +5 = 2x + 2h +5
f(x) = 2x + 5
 
f(x+h) - f(x) = 2x + 2h + 5 - 2x - 5 = 2h
 
[f(x+h) - f(x)]/h = 2h/h = 2
 
:)