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3 years ago

Algebra 2B U2 L6 Function Operations practice 8-10

Mathematics

1 answer:

Bess [88]3 years ago

6 0

Answer:

1) f(g(0)) = 0

2) g(f(2)) = 2

3) g(g(0)) = 8

Step-by-step explanation:

Here, the given functions are:

g(x) = 3 x +2 and f(x)= (x-2)/3

1. Now, f(g(x)) = f(3x+2)

Also, f(3x+2) = (3x+2 -2) /3 = x

So, f(g(x)) = x

⇒ f(g(0)) = 0

2. g(f(x)) = g((x-2)/3) = 3((x-2)/3) +2

or, g(f(x)) = x

⇒ g(f(2)) = 3((2)-2/3) +2 = 2

or, g(f(2)) = 2

3. g(g(0)= g( 3 (0) +2) = g(2)

Now, g(2) = 3(2) + 2 = 6 + 2 = 8

or, g(g(0)) = 8

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Find the measures of the complementary angles that satisfy each case. One of the angles is 3 times larger than the other.

Nookie1986 [14]

Answer:

22.5° and 67.5°

Step-by-step explanation:

The sum of complementary angles equal 90°.

Given that one of the complementary angles is 3 times larger than the other, let "x" represent the other angle.

Thus, the following expression can be written to represent this case:

$x + 3x = 90$

Solve for x

$4x = 90$

Divide both sides by 4

$\frac{4x}{4} = \frac{90}{4}$

$x = 22.5$

The measure of the complementary angles are:

x = 22.5°

3x = 3(22.5) = 67.5°

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3 years ago

F(x)= -1/3x+13 when value is f(-3)

almond37 [142]

Answer:

Step-by-step explanation:

f(x)=-1/3x+13

f(-3)=-1/3(-3)+13

f(-3)=3/3+13

f(-3)=1+13

f(-3)=14

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2 years ago

On a particular Saturday, 60% of the visitors to an art museum were students. If 144 visited the museum, how many total visitors

Bad White [126]

Answer:

240 visitors

Step-by-step explanation:

We are given the following in the question:

Percentage of visitors that are student to art museum = 60%

Total number of students to museum = 144

We have to find the total number of visitors to the museum.

Let x be the total number of visitors to the museum.

Thus, we can write the equation:

$60\%\times x = 144\\\\\dfrac{60}{100}\times x = 144\\\\\Rightarrow x = 144\times \dfrac{100}{60}\\\\\Rightarrow x = 240$

Thus, there were 240 visitors to the art museum on that day.

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3 years ago

At which of the following points do the two equations f(x)=3x2+5 and g(x)=4x+4 intersect?

Basile [38]

Answer:

( $\frac{1}{3}$ , $\frac{16}{3}$ ) and (1, 8 )

Step-by-step explanation:

To find the points of intersection equate f(x) and g(x), that is

3x² + 5 = 4x + 4 ( subtract 4x + 4 from both sides )

3x² - 4x + 1 = 0 ← in standard form

(3x - 1)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

3x - 1 = 0 ⇒ 3x = 1 ⇒ x = $\frac{1}{3}$

x - 1 = 0 ⇒ x = 1

Substitute these values into either of the 2 functions for corresponding y- coordinates.

Substituting into g(x), then

g(1) = 4(1) + 4 = 4 + 4 = 8 ⇒ (1, 8 )

g( $\frac{1}{3}$ ) = $\frac{4}{3}$ + 4 = $\frac{16}{3}$ ⇒ ( $\frac{1}{3}$ , $\frac{16}{3}$ )

3 0

3 years ago

Evaluate

lakkis [162]

A piece-wise function combines more than one functions of different input values.

The value of f(-1) is -3

From the graph, we have the following observations

When x = -1, y = -3
When x = -1, y = -4

Notice that there is a closed circle at the point where x = -1 and y = -3.

This means that y = -3 is inclusive of the values of y on that particular function

However, there is an open circle at the point where x = -1 and y = -3.

This means that y = -4 is exclusive of the values of y on that particular function

The correct corresponding value of y is when y is inclusive.

Hence, the value of f(-1) is -3

See attachment for the graph of the piece-wise functions

Read more about piece-wise functions at:

brainly.com/question/11547854

6 0

3 years ago