Show that is linear of slope m if and only if (x + h) (x)
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Show that ƒ is linear of slope m if and only if ƒ(x + h) − ƒ(x) = mh (for all x and h).
That is to say, prove the following two statements:
(a) ƒ is linear of slope m implies that ƒ(x + h) − ƒ(x) = mh (for all x and h).
(b) ƒ (x + h) − ƒ(x) = mh (for all x and h) implies that ƒ is linear of slope m.
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