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3 years ago

Given the following functions f(x) and g(x), solve f[g(6)]. f(x) = 6x + 12 g(x) = x − 8

Mathematics

2 answers:

iogann1982 [59]3 years ago

6 0

Answer:

Answer:

Option 2nd is correct.

=0.

Step-by-step explanation:

Given the function:

Solve:

First calculate:

f[g(x)]

Substitute the function g(x)

Replace x with x-8 in the function f(x) we get;

The distributive property says that:

Using distributive property:

⇒

Put x = 6 we get;

Therefore, the value of is 0.

Step-by-step explanation:

dalvyx [7]3 years ago

5 0

Answer:

Step-by-step explanation:

f(x) = 6x + 12

g(x) = x − 8

f(g(6))=?

g(6)=6-8= -2

f(-2)= -2*6+12= -12+12=0

f(g(6))= f(-2)=0

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Answer:

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3 years ago

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What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1? PLs HELP!!

Delicious77 [7]

ANSWER
$f(x)= \frac{1}{4} {(x - 1)}^{2}$

EXPLANATION

Since the directrix is
$y = - 1$

the axis of symmetry of the parabola is parallel to the y-axis.

Again, the focus being,

$(1,1)$

also means that the parabola will open upwards.

The equation of parabola with such properties is given by,

${(x - h)}^{2} = 4p(y - k)$
where
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is the vertex of the parabola.

The directrix and the axis of symmetry of the parabola will intersect at
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The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.

This implies that,
$h = \frac{1 + 1}{2} = 1$

and
$k = \frac{ - 1 + 1}{2} = 0$

The equation of the parabola now becomes,

$(x - 1) ^{2} = 4p(y - 0)$

$|p| = 1$

Thus, the distance between the vertex and the directrix.

This means that,

$p = - 1 \: or \: 1$

Since the parabola opens up, we choose
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Our equation now becomes,

${(x - 1)}^{2} = 4(1)(y - 0)$

This simplifies to
${(x - 1)}^{2} = 4y$

or

$y = \frac{1}{4} {(x - 1)}^{2}$

This is the same as,

$f(x)= \frac{1}{4} {(x - 1)}^{2}$

The correct answer is D .

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3 years ago

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Tatiana [17]

Answer:

divide 2 by three to know how many you can solve in one min= 2/3= .67

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You can solve 18 problems in 12 min!!

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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3 years ago

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densk [106]

Answer:

Step-by-step explanation:

You could factor this to find out how many real roots you have, but it's easier to use the rule of the discriminate. The discriminate comes from the quadratic formula:

$b^2-4ac$

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discriminate < 0, you have 2 imaginary roots

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$8^2-4(6)(-7)=232$

Because 232 is > 0, we have 2 real roots.

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3 years ago