Given the function #f(x)=-3-x#, how do you express the value of #(f(x+h)-f(x))/h#?

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Answer 1 · 2018-05-06T07:37:03

#-1#

#(-3-(x+h)-(-3-x))/h#

#=(cancel(-3)cancel(-x)-hcancel(+3)cancel(+x))/h=(-h)/h=-1#

Answer 2 · 2018-05-06T07:40:16

See explanation.

If #f(x)=-3-x# then we can write that:

#f(x+h)=-3-(x+h)=-3-x-h#

#f(x)=-3-x#

Combining the two expressions we get:

#(f(x+h)-f(x))/h=(-3-x-h-(-3-x))/h=#

#(-3-x-h+3+x)/h=(-h)/h=-1#