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Artyom0805 [142]
3 years ago
8

If h(x) = (f o g)(x) and h(x) = sqrt(x+5), find g(x) if f(x) = sqrt(x+2)

Mathematics
1 answer:
agasfer [191]3 years ago
7 0

Answer:

  • g(x) = x + 3

Step-by-step explanation:

<h3>Given</h3>
  • h(x) = (f ο g)(x)
  • h(x) = \sqrt{x+5}
  • f(x) = \sqrt{x+2}
<h3>To find</h3>
  • g(x)
<h3>Solution</h3>

<u>We know that:</u>

  • (f ο g)(x) = f(g(x))

<u>Substitute x with g(x) and solve for g(x):</u>

  • \sqrt{x+5} = \sqrt{g(x)+2}
  • x + 5 = g(x) + 2
  • x + 3 = g(x)
  • g(x) = x + 3
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Which graph is an example of a function whose parent graph is of the form y = √x?
Maksim231197 [3]

Answer:

The correct option is 1.

Step-by-step explanation:

The given parent function is

y=\sqrt{x}

1. Domain of the function is all positive real number including 0.

2. Range of the function is all positive real number including 0.

3. It is an increasing function. It increases at decreasing rate.

First graph increase at decreasing rate and it starts from (-4,-1), therefore the required function is

y=\sqrt{x+4}-1

Therefore graph 1 is an example of a function whose parent graph is of the form y = √x.

Second graph is a parabola, so it is the graph of a quadratic function.

Third graph is a rectangular hyperbola, so it is the graph of a rational functions.

Fourth graph is increasing at increasing rate, so it is the graph of an exponential function.

Therefore options 2, 3 and 4 are incorrect.

6 0
3 years ago
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The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number
andreyandreev [35.5K]

Answer:

39

Step-by-step explanation:

let the 2 digit number be ab = 10a + b ( considering place value )

The reversed  2 digit number is ba = 10b + a

The sum of the 2 digit number is

a + b = 12 ( subtract b from both sides )

a = 12 - b → (1)

Expressing as an equation

ba = ab + 54 , that is

10b + a = 10a + b + 54

Substitute a = 12 - b into the equation

10b + 12 - b = 10(12 - b) + b + 54 , simplify both sides

9b + 12 = 120 - 10b + b + 54

9b + 12 = - 9b + 174 ( add 9b to both sides )

18b + 12 = 174 ( subtract 12 from both sides )

18b = 162 ( divide both sides by 18 )

b = 9

Substitute b = 9 into (1)

a = 12 - 9 = 3

Thus

the original 2 digit number = ab = 39

The reversed 2 digit number = ba = 93

which is 54 more than the original number

7 0
3 years ago
If ∠C and ∠D are vertical angles and m ∠ C = x + 5 and m ∠ D = –2x + 80, what is m ∠ C?
amm1812

Answer:

m∠C=30°

Step-by-step explanation:

we know that

<u>Vertical Angles</u> are the angles opposite each other when two lines cross. They are always equal

so

m∠C=m∠D

substitute the given values

(x+5)\°=(-2x+80)\°

Solve for x

x+2x=80-5\\3x=75\\x=25

<em>Find the measure of angle C</em>

m∠C=(x+5)°

substitute the value of x

m∠C=(25+5)=30°

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2 years ago
3x/5=30 solve the equation
Bess [88]

Answer:

Step-by-step explanation:

To solve equations like this you need to to get x by itself.

So, Let's multiply both sides by 5 to get rid of 5.

3x/5 *5 = 30 * 5

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Now we divide both sides by 3 to get x by itself,

3x/3 = 150/3

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What is an equation of the line that passes through the point (1,-3) and is perpendicular to the line x+3y=21
docker41 [41]

The linear equation that is perpendicular to the line x+3y=21 is:

y = 3*x - 6

<h3>How to find the equation of the line?</h3>

A general line in the slope-intercept form is written as:

y = m*x + b

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Two linear equations are perpendicular if the product between the two slopes is equal to -1.

Rewriting the given line we can get:

x +3y = 21

3y = 21 - x

y = 21/3 - x/3

y = (-1/3)*x + 21/3

Then the slope is (-1/3), if our line is perpendicular to this one, then:

m*(-1/3) = -1

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our line is:

y = 3*x + b

To find the value of b, we use the fact that our line passes through (1, - 3)

-3 = 3*1 + b

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-6 = b

The line is y = 3*x - 6

Learn more about linear equations:

brainly.com/question/1884491

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