Please, evaluate and simplify different quotients: f(x+h)−f(x)h, where h≠0 and f(x)−f(a)x−a where x≠a for each of the following functions: f(x)=x2−2x; f(x)=4−5x; f(x)=x3+2; f(x)=7x+3

The first one: f(x+h)−f(x)h=(x+h)2−2(x+h)−(x2−2x)h=x2+h2+2xh−2x−2h−x2+2xh=h2+2xh−2hh=2xh+h2h−2hh=2x+h−2

I did the second: f(x)=4−5x f(x+h)−f(x)h=4−5(x+h)−(4−5x)h=4−5x+5x−5h−4h=−5hh=−5

The first one: f(x+h)−f(x)h=(x+h)2−2(x+h)−(x2−2x)h=x2+h2+2xh−2x−2h−x2+2xh=h2+2xh−2hh=2xh+h2h−2hh=2x+h−2

I did the second: f(x)=4−5x f(x+h)−f(x)h=4−5(x+h)−(4−5x)h=4−5x+5x−5h−4h=−5hh=−5

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High School
Algebra
Algebra I
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osula9a

Answered question

2021-12-11

Please, evaluate and simplify different quotients:
$\frac{f (x + h) - f (x)}{h}$ , where $h \neq 0$ and $\frac{f (x) - f (a)}{x - a}$ where $x \neq a$ for each of the following functions:
$f (x) = x^{2} - 2 x$ ;
$f (x) = 4 - 5 x$ ;
$f (x) = x^{3} + 2$ ;
$f (x) = \frac{7}{x + 3}$