QuestionFind and simplify for $f(x)=7x-2$ : (A) $f(x+h)$ , (B) $f(x+h)-f(x)$ , (C) $\frac{f(x+h)-f(x)}{h}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=7x-$ . We are asked to find and simplify $f(x+h)$ , $f(x+h)-f(x)$ , and $\frac{f(x+h)-f(x)}{h}$

STEP 2

First, we need to find $f(x+h)$ . We can do this by replacing every instance of $x$ in the function $f(x)$ with $(x+h)$ .
$f(x+h) =7(x+h) -2$

STEP 3

Now, distribute the $7$ to both $x$ and $h$ inside the parentheses.
$f(x+h) =7x +7h -2$

STEP 4

Now, we need to find $f(x+h)-f(x)$ . We can do this by subtracting $f(x)$ from $f(x+h)$ .
$f(x+h)-f(x) = (7x +7h -2) - (7x -2)$

STEP 5

implify the expression by performing the subtraction.
$f(x+h)-f(x) =7h$

STEP 6

Now, we need to find $\frac{f(x+h)-f(x)}{h}$ . We can do this by dividing $f(x+h)-f(x)$ by $h$ .
$\frac{f(x+h)-f(x)}{h} = \frac{h}{h}$

STEP 7

implify the expression by cancelling out the $h$ in the numerator and the denominator.
$\frac{f(x+h)-f(x)}{h} =7$ So, we have found that(A) $f(x+h) =7x +7h -2$ (B) $f(x+h)-f(x) =7h$ (C) $\frac{f(x+h)-f(x)}{h} =7$

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QuestionFind and simplify for $f(x)=7x-2$ : (A) $f(x+h)$ , (B) $f(x+h)-f(x)$ , (C) $\frac{f(x+h)-f(x)}{h}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=7x-$ . We are asked to find and simplify $f(x+h)$ , $f(x+h)-f(x)$ , and $\frac{f(x+h)-f(x)}{h}$

STEP 2

First, we need to find $f(x+h)$ . We can do this by replacing every instance of $x$ in the function $f(x)$ with $(x+h)$ .
$f(x+h) =7(x+h) -2$

STEP 3

Now, distribute the $7$ to both $x$ and $h$ inside the parentheses.
$f(x+h) =7x +7h -2$

STEP 4

Now, we need to find $f(x+h)-f(x)$ . We can do this by subtracting $f(x)$ from $f(x+h)$ .
$f(x+h)-f(x) = (7x +7h -2) - (7x -2)$

STEP 5

implify the expression by performing the subtraction.
$f(x+h)-f(x) =7h$

STEP 6

Now, we need to find $\frac{f(x+h)-f(x)}{h}$ . We can do this by dividing $f(x+h)-f(x)$ by $h$ .
$\frac{f(x+h)-f(x)}{h} = \frac{h}{h}$

STEP 7

implify the expression by cancelling out the $h$ in the numerator and the denominator.
$\frac{f(x+h)-f(x)}{h} =7$ So, we have found that(A) $f(x+h) =7x +7h -2$ (B) $f(x+h)-f(x) =7h$ (C) $\frac{f(x+h)-f(x)}{h} =7$

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QuestionFind and simplify for f(x)=7x−2f(x)=7x-2f(x)=7x−2: (A) f(x+h)f(x+h)f(x+h), (B) f(x+h)−f(x)f(x+h)-f(x)f(x+h)−f(x), (C) f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=7x−f(x)=7x-f(x)=7x− . We are asked to find and simplify f(x+h)f(x+h)f(x+h), f(x+h)−f(x)f(x+h)-f(x)f(x+h)−f(x), and f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​

STEP 2

First, we need to find f(x+h)f(x+h)f(x+h). We can do this by replacing every instance of xxx in the function f(x)f(x)f(x) with (x+h)(x+h)(x+h).f(x+h)=7(x+h)−2f(x+h) =7(x+h) -2f(x+h)=7(x+h)−2

STEP 3

Now, distribute the 777 to both xxx and hhh inside the parentheses.f(x+h)=7x+7h−2f(x+h) =7x +7h -2f(x+h)=7x+7h−2

STEP 4

Now, we need to find f(x+h)−f(x)f(x+h)-f(x)f(x+h)−f(x). We can do this by subtracting f(x)f(x)f(x) from f(x+h)f(x+h)f(x+h).f(x+h)−f(x)=(7x+7h−2)−(7x−2)f(x+h)-f(x) = (7x +7h -2) - (7x -2)f(x+h)−f(x)=(7x+7h−2)−(7x−2)

STEP 5

implify the expression by performing the subtraction.f(x+h)−f(x)=7hf(x+h)-f(x) =7hf(x+h)−f(x)=7h

STEP 6

Now, we need to find f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​. We can do this by dividing f(x+h)−f(x)f(x+h)-f(x)f(x+h)−f(x) by hhh.f(x+h)−f(x)h=hh\frac{f(x+h)-f(x)}{h} = \frac{h}{h}hf(x+h)−f(x)​=hh​

STEP 7

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QuestionFind and simplify for $f(x)=7x-2$ : (A) $f(x+h)$ , (B) $f(x+h)-f(x)$ , (C) $\frac{f(x+h)-f(x)}{h}$ .

Assumptions1. The function is $f(x)=7x-$ . We are asked to find and simplify $f(x+h)$ , $f(x+h)-f(x)$ , and $\frac{f(x+h)-f(x)}{h}$

First, we need to find $f(x+h)$ . We can do this by replacing every instance of $x$ in the function $f(x)$ with $(x+h)$ .
$f(x+h) =7(x+h) -2$

Now, distribute the $7$ to both $x$ and $h$ inside the parentheses.
$f(x+h) =7x +7h -2$

Now, we need to find $f(x+h)-f(x)$ . We can do this by subtracting $f(x)$ from $f(x+h)$ .
$f(x+h)-f(x) = (7x +7h -2) - (7x -2)$

implify the expression by performing the subtraction.
$f(x+h)-f(x) =7h$

Now, we need to find $\frac{f(x+h)-f(x)}{h}$ . We can do this by dividing $f(x+h)-f(x)$ by $h$ .
$\frac{f(x+h)-f(x)}{h} = \frac{h}{h}$