Answer:
Step-by-step explanation:
If 
, then 
. It follows that
![\begin{aligned} \\\frac{g(x+h)-g(x)}{h} &= \frac{1}{h} \cdot [g(x+h) - g(x)] \\&= \frac{1}{h} \left( \frac{1}{x+h} - \frac{1}{x} \right)\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5C%5C%5Cfrac%7Bg%28x%2Bh%29-g%28x%29%7D%7Bh%7D%20%26%3D%20%5Cfrac%7B1%7D%7Bh%7D%20%5Ccdot%20%5Bg%28x%2Bh%29%20-%20g%28x%29%5D%20%5C%5C%26%3D%20%5Cfrac%7B1%7D%7Bh%7D%20%5Cleft%28%20%5Cfrac%7B1%7D%7Bx%2Bh%7D%20-%20%5Cfrac%7B1%7D%7Bx%7D%20%5Cright%29%5Cend%7Baligned%7D)
Technically we are done, but some more simplification can be made. We can get a common denominator between 1/(x+h) and 1/x.
Now we can cancel the h in the numerator and denominator under the assumption that h is not 0.
I think 4. is 2 and 4. but I'm not entirely sure because I haven't done factors in a long time.
Answer:
x(x^2+2)^3/2
Step-by-step explanation:
y'=1/2(x^2+2)^3/2.2x
= x(x^2+2)^3/2
By applying concepts of <em>linear</em> functions, the graphs are related to the following expressions:
- (4/7) · x + 2
- x + 2
- (1/7) · x + 2
- - (1/7) · x + 2
- - x + 2
<h3>How to match a line with a given linear function</h3>
Graphically speaking, lines are described by <em>linear</em> functions, a kind of polynomials of grade 1, whose standard form is presented below:
y = m · x + b (1)
Where:
- x - Independent variable
- y - Dependent variable
- m - Slope
- b - Intercept
Please notice that the slope is represented graphically by the change in the y-variable divided by the change in the x-variable and the intercept is the location where the line passes through the y-axis. Hence, the <em>resulting</em> expressions are shown in this order:
- (4/7) · x + 2
- x + 2
- (1/7) · x + 2
- - (1/7) · x + 2
- - x + 2
To learn more on linear functions: brainly.com/question/9330192
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Since you know the value of "x", you can plug in the value for "x" in the equation.
[When an exponent is negative, you move it to the other side of the fraction to make the exponent positive.]
For example:
or 
or y³
x = -2
f(x) = 9x + 7
f(-2) = 9(-2) + 7 = -18 + 7 = -11
(idk if you should have it as a decimal or a fraction)
x = -1
f(x) = 9x + 7
f(-1) = 9(-1) + 7 = -9 + 7 = -2
x = 0
f(x) = 9x + 7
f(0) = 9(0) + 7 = 7
x = 1
f(x) = 9x + 7
f(1) = 9(1) + 7 = 9 + 7 = 16
x = 2
f(x) = 9x + 7
f(2) = 9(2) + 7 = 18 + 7 = 25
You need to determine the solution of f(x) = g(x)
Since you know f(x) = 9x + 7 and , you can plug in (9x + 7) for f(x), and (
) into g(x)
f(x) = g(x)
You can plug in each value of x into the equation
Your answer is x = 2 because when you plug in 2 for x in the equation, you get 25 = 25
