Question

If ƒ(x ) = 3x + 1, then ƒ(a + h ) - ƒ(a ) =

h
3h
3h + 2

Answer 1

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If  $\mathsf{f(x)=3x+1,}$  then

$\mathsf{f(a+h)-f(a)}\\\\ =\mathsf{\big[3(a+h)+1]-(3a+1)}\\\\ =\mathsf{\big[3a+3h+1]-3a-1}\\\\ =\mathsf{\diagup\!\!\!\!\! 3a+3h+\diagdown\!\!\!\! 1-\diagup\!\!\!\!\! 3a-\diagdown\!\!\!\! 1}\\\\ =\mathsf{3h}\quad\longleftarrow\quad\textsf{this is the answer.}$


I hope this helps. =)