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Leviafan [203]
3 years ago
10

Use f(x)=(2x+1)/(3x-2) and g(x)=5x-1 to find (gof)(x)

Mathematics
1 answer:
Orlov [11]3 years ago
5 0

Answer:

From the functions f(x) and g(x) we have (g\circ f)(x)=\frac{7(x+1)}{3x-2}

Step-by-step explanation:

Given that the functions f is defined by f(x)=\frac{2x+1}{3x-2}

and g is g(x)=5x-1

To find the (g\circ f)(x) :

(g\circ f)(x)=g(f(x))

=g(\frac{2x+1}{3x-2})

=5(\frac{2x+1}{3x-2})-1

=\frac{10x+5}{3x-2}-1

=\frac{10x+5-1(3x-2)}{3x-2} ( by using the distributive property )

=\frac{10x+5-3x+2}{3x-2}

=\frac{7x+7}{3x-2} ( adding the like terms )

=\frac{7(x+1)}{3x-2}

Therefore (g\circ f)(x)=\frac{7(x+1)}{3x-2}.

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Andre45 [30]
<h3>Answer: The average rate of change for both is -2</h3>

=======================================================

Explanation:

The x interval [0,3] is the same as writing 0 \le x \le 3

It starts at x = 0 and ends at x = 3.

The graph shows that x = 0 leads to y = 3. So we have the point (0,3) on the parabola. We also have the point (3,-3) on the parabola.

Let's find the slope of the line through these endpoints.

(x_1,y_1) = (0,3) \text{ and } (x_2,y_2)  = (3,-3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-3 - 3}{3 - 0}\\\\m = \frac{-6}{3}\\\\m = -2\\\\

The slope is -2. This is the average rate of change from x = 0 to x = 3.

This is because:

slope = rise/run = (change in y)/(change in x) = average rate of change.

-------------

Now let's find the slope for the table.

Focus on the rows for x = 0 and x = 3. They lead to f(x) = 10 and f(x) = 4 respectively.

We have (0,10) and (3,4) as our two points this time.

(x_1,y_1) = (0,10) \text{ and } (x_2,y_2)  = (3,4)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{4 - 10}{3 - 0}\\\\m = \frac{-6}{3}\\\\m = -2\\\\

We get the same slope as before, so we have the same rate of change.

Notice the change in y (-6) is the same as before. So we could pick any two y values we want as long as there's a gap of 6 between them, and the second y value is smaller than the first.

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2 years ago
Petra jogs 2 miles in 24 minutes. At this rate, how long would it take her to jog 10 miles?
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Step-by-step explanation:

24 minutes / 2 miles = 12 minutes / 1 mile

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Cross multiply

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Hope that helps!

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3 years ago
Tyre measured the average monthly temperature in degrees Fahrenheit for several months. If February is set ect 2 and June is oud
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Answer:

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Step-by-step explanation:

7 0
3 years ago
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Step-by-step explanation:

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3 years ago
Determine which of the following numbers could not represent the probability of an event. Explain your reasoning. (a). 33.3% (b)
statuscvo [17]

Answer:

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Step-by-step explanation:

The simple golden rule that we need to know here is

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<em><u /></em>

If an event has a probability of p(x), we can say:

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Also, probability is ALWAYS POSITIVE.

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C) 0.0002 is in between 0 and 1, so possible

D) 0 probability means it can't happen, so that's okay as well

E) this is a fraction with numerator less than denominator, which means its between 0 and 1, so OK

F) this fraction's numerator is greater than denominator, so it's greater than 1. Probability can't be greater than 1, so NOT OK

Out of these B and F cannot represent the probability of an event

6 0
3 years ago
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