Consider these functions:

f(x)= -1/2x^2 + 5x
g(x)= x^2 + 2

What is the value of f(g(-2))?

Answers

Answer 1

Answer:

The value of f(g(-2)) is 12.

Step-by-step explanation:

We'll start by solving g(-2):

[tex]g(-2)\\= (-2)^2 + 2\\= 4 + 2\\= 6[/tex]

Now we can take that value and plug it into function f:

[tex]f(6)\\= \frac{-1}{2}6^2 + 5 * 6\\= -36/2 + 30\\= -18 + 30\\= 12[/tex]

Alternatively, you can work out a new single function that in itself describes f(g())

[tex]f(g(x)) = -\frac{1}{2}g(x)^2 + 5g(x)\\= -\frac{1}{2}(x^2 + 2)^2 + 5(x^2 + 2)\\= -\frac{1}{2}(x^4 + 4x^2 + 4) + 5x^2 + 10\\= -\frac{1}{2}x^4 - 2x^2 - 2 + 5x^2 + 10\\= -\frac{x^4}{2} + 3x^2 + 8[/tex]

and try plugging -2 into the new function

[tex]= - \frac{-2^4}{2} + 3(-2)^2 + 8\\= -16 / 2 + 3 * 4 + 8\\= -8 + 12 + 8\\= 12[/tex]

Answer 2

The value of f(g(-2)) for the given expression will be 12.

What is an expression?

Expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

We have,

f(x) = [tex]\frac{-1}{2} x^2[/tex]  + 5x

And,

g(x) = x² + 2

Now,

For, x = -2,

i.e.

g(x) = x² + 2

Now,

Substituting the value of x = -2,

g(-2) = (-2)² + 2

On solving,

We get,

g(-2) =  6

Now,

For, f(g(-2)),

f(x) = [tex]\frac{-1}{2} x^2[/tex]  + 5x

i.e.

Substituting the value of g(-2) =  6,

i.e.

f(g(-2)) = [tex]\frac{-1}{2} (g(-2)^2)[/tex] + 5(g(-2))

i.e.

f(g(-2)) = [tex]\frac{-1}{2} *6^2[/tex]  + 5 * 6

On solving,

We get,

f(g(-2)) = -18 + 30

i.e.

f(g(-2)) = 12

So, the value of f(g(-2)) for the given expression is 12.

Hence, we can say that the value of f(g(-2)) for the given expression will be 12.

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Answers

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Shipping = 2 percent of Total Cost

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Answers

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Step-by-step explanation:

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Answers

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Find the equation of the linear function represented by the table below in slope-
intercept form.
X
O
1
2
3
4
y
6
14
22
30
38
Answer: y =
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Answer:

yo done so easy

Step-by-step explanation:

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Answers

Answer:

r=-1/2

Step-by-step explanation:

(-5*-1/2=2.5)( 2.5-1=1.5) (7x -1/2= -3.5)-3.5+5 =1.5

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Answers

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Answers

Answer:

0.5

Step-by-step explanation:

A and B are independent events.
PA) = 0.6
P(B) = 0.4
What is P(AB)?
O A. 0.24
B. 0.6
O c.0.4
D. Not enough information

Answers

Answer:

not enough information

Answer:

It's 0.6

Step-by-step explanation:

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Answers

Answer:

x=14, y=37

Step-by-step explanation:

We know that (4y-10)° and 3x° are supplementary angles, meaning the total sum of the angles add up to 180°. (4y-10)° is also corresponding to the blank angle below (9x+12)°, making it a vertical angle. Since (4y-10)°=(9x+12)° because they are vertical angles, then that means we can solve for x:

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Rewrite 7 − 8 using the additive inverse and display the new expression on a number line.

Select one:

a.
7 + (−8)
An image of a horizontal number line is shown with labels from negative 2 to positive 8. An arrow begins at 0 and ends at 7. Another arrow begins at 7 and ends at negative 1.


b.
7 + 8
An image of a horizontal number line is shown with labels from 0 to 15. An arrow begins at 0 and ends at 7. Another arrow begins at 7 and ends at 15.


c.
7 − (−8)
An image of a horizontal number line is shown with labels from 0 to 15. An arrow begins at 0 and ends at 7. Another arrow begins at 7 and ends at 15.


d.
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Answers

Answer:

[tex]7 + (-8)[/tex]

Step-by-step explanation:

Given

[tex]7 - 8[/tex]

(a): Write as additive inverse.

An additive inverse is of the form a + (-b)

In this case:

[tex]a = 7[/tex]

[tex]b = -8[/tex]

So, the expression can be represented as:

[tex]7 + (-8)[/tex]

(b): Number line representation

When the expression in (a) is solved.

The result is:

[tex]7 - 8 = 7 + (-8) = -1[/tex]

This means that the number line must accommodate 7 and -1.

Having said that, options (b) and (c) are out because their range is 0 to 15 and this excludes -1.

Option (d) is a wrong representation of [tex]7 - 8[/tex]

Hence, (a) is correct

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Answers

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Answers

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Answers

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Step-by-step:

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Answers

Answer:

Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Answers

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Answers

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Answers

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Step-by-step explanation:

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Answers

Answer:

The answer is 15*5=75.

Step-by-step explanation:

So to get the answer you need to know how many calories are in a ounce of yogurt which is 15. Then you you multiply 15*5 to get how many calories are in a 5 ounce of yogurt. When you solve 15*5=75, use either  a calculator or solve it down on paper. To know that you got the right answer for 15*5= 75 please punch it in on a calculator. I hope this helps if you need any more clarificatio please comment! Thanks!

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