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

Answer 1

Hazel Anglin

#-1#

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

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

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Answer 2

Genesis Allen

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#

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Answer 3

Eva Adamson

To express the value of ((f(x+h)-f(x))/h) for the function (f(x)=-3-x), we substitute (f(x+h)) and (f(x)) into the expression:

[ \frac{f(x+h)-f(x)}{h} = \frac{(-3-(x+h))-(-3-x)}{h} ]

Now, simplify the expression:

[ \frac{(-3-x-h)-(-3-x)}{h} = \frac{-3-x-h+3+x}{h} = \frac{-h}{h} ]

Finally, cancel out (h) in the numerator and denominator:

[ \frac{-h}{h} = -1 ]

So, the value of ((f(x+h)-f(x))/h) for the given function is (-1).

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Answer from HIX Tutor

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