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2 years ago

Find f (-2) f(x)= 3x^2 - 8x + 7

Mathematics

1 answer:

Maslowich2 years ago

8 0

Answer: Solving for f. Want to solve for x instead?

1 Remove parentheses.

f\times -2fx=3{x}^{2}-8x+7f×−2fx=3x

 −8x+7

2 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

 x

 =x

a+b

 .

-{f}^{2}\times 2x=3{x}^{2}-8x+7−f

 ×2x=3x

 −8x+7

3 Regroup terms.

-2{f}^{2}x=3{x}^{2}-8x+7−2f

 x=3x

 −8x+7

4 Divide both sides by -2−2.

{f}^{2}x=-\frac{3{x}^{2}-8x+7}{2}f

 x=−

3x

 −8x+7

5 Divide both sides by xx.

{f}^{2}=-\frac{\frac{3{x}^{2}-8x+7}{2}}{x}f

 =−

3x

 −8x+7

6 Simplify \frac{\frac{3{x}^{2}-8x+7}{2}}{x}

3x

 −8x+7

 to \frac{3{x}^{2}-8x+7}{2x}

2x

3x

 −8x+7

 .

{f}^{2}=-\frac{3{x}^{2}-8x+7}{2x}f

 =−

2x

3x

 −8x+7

7 Take the square root of both sides.

f=\pm \sqrt{-\frac{3{x}^{2}-8x+7}{2x}}f=±√

−

2x

3x

 −8x+7

8 Simplify \sqrt{-\frac{3{x}^{2}-8x+7}{2x}}√

−

2x

3x

 −8x+7

 to \sqrt{\frac{3{x}^{2}-8x+7}{2x}}\imath√

2x

3x

 −8x+7

 ı.

f=\pm \sqrt{\frac{3{x}^{2}-8x+7}{2x}}\imathf=±√

2x

3x

 −8x+7

 ı

9 Regroup terms.

f=\pm \imath \sqrt{\frac{3{x}^{2}-8x+7}{2x}}f=±ı√

2x

3x

 −8x+7

Done- :)

f=±ı√ 2x 3x 2 −8x+7

Step-by-step explanation

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2 years ago

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In the graph attached with the question, at point (0,6) the curve crosses the y-axis. Therefore, the y-intercept (s-intercept) in this case is 6. It means that in year 2000 (t=0), 6 hundred shirts were sold.

However, there is no point on the graph where the curve crosses the x-axis, meaning there is no x-intercept (t-intercept). It means that there is not a single year when the number of shirts sold is 0.

(PART B): As you can see in the graph (attached with the question) that the f(t) is increasing (exponentially) with the increase in t. Therefore, we can safely say that as t increases without bound, the f(t) increases (also). In this context, it means that the sale of shirts increases as the years go by. Hence, the correct blank is "increases."

(PART C): The average rate of change is actually the slope. To find the slope, we can use the following formula:

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Given points: (5, 12.5) and (7, 22). Plug the values in equation (X),

slope = $\frac{22-12.5}{7-5} = 4.75$

Hence, the average rate of change for the function between t=5 and t=7 is 4.75 (answer).

(PART D): This part is bit tricky. Therefore, read the explanation carefully!

You can see in the graph that number of Shirts sold is in hundreds. It means that 1 unit (of y-axis in a graph) represents 100 shirts. Therefore, as in the question it is mentioned that there are 1000 T-shirts sold, it will become 10 units (since 10*100 = 1000). So, the function g(t) will become the following:

$g(t) = f(t) + 10$ --- (Y)

Why did I add f(t)? Because in the question, the word "and" is underlined. It means that g(t) represents not only 1000 T-shirts (10*100 = 1000) sold at the basketball games each year, but it also has the number of T-shirts sold ONLINE, which is f(t).

Now insert f(t) in (Y) and solve:

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