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2 years ago

Let f(x)=e^x and G(x)=x+6. What are the domain and range of g(f(x))?

Mathematics

1 answer:

Lena [83]2 years ago

3 0

Answer:

Domain and Range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively

Step-by-step explanation:

We have the functions, f(x) = eˣ and g(x) = x+6

So, their composition will be g(f(x)).

Then, g(f(x)) = g(eˣ) = eˣ+6

Thus, g(f(x)) = eˣ+6.

Since the domain and range of f(x) = eˣ are all real numbers and positive real numbers respectively.

Moreover, the function g(f(x)) = eˣ+6 is the function f(x) translated up by 6 units.

Hence, the domain and range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.

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How to find the area of a square ABC D

____ [38]

Answer:

The answer to your question is 13 u²

Step-by-step explanation:

We know that the small triangle is surrounded by right triangles so we can use the Pythagorean theorem to find the lengths of the small triangle

AD² = 3² + 2²

Simplify

AD² = 9 + 4

AD² = 13

AD = $\sqrt{13}$

Find the area of the square

Area = side x side

Area = AD x AD

Area = $\sqrt{13} x \sqrt{13}$

Area = 13 u²

6 0

3 years ago

There are 7 ushers and 11 technicians helping at the Harper Middle School fall play.

bearhunter [10]

Answer:

<h3>The ratio of technicians to all helpers is 11 : 7, or $\frac{11}{7}$ or 11 to 7.</h3>

Step-by-step explanation:

Given that there are 7 ushers and 11 technicians helping at the Harper Middle School fall play.
Let x be the number of ushers ( or helpers ).
Therefore x=7 helpers.
Let y be the number of technicians.
Therefore y=11 technicians.

<h3>To find the ratio of technicians to all helpers :</h3>

That is to find the ratio of y to x.

We can write the ratio of technicians to all ushers(helpers) as y : x

Which implies that 11 : 7, (since y=11 and x=7)

Or $\frac{11}{7}$ or 11 to 7

<h3>The ratio of technicians to all helpers is 11 : 7, or $\frac{11}{7}$ or 11 to 7</h3>

4 0

3 years ago

A pet store sells goldfish and hermit crabs,

Elis [28]

Answer:

$Cost = \$28$

Step-by-step explanation:

Given

Represent Goldfish with g and hermit crabs with h.

The first statement, we have:

$7g + 3h = 26$

The second statement, we have:

$4g + 5h = 28$

Required

Determine the selling price of 6 goldfish and 4 hermit crabs

The equations are:

$7g + 3h = 26$ --- (1)

$4g + 5h = 28$ --- (2)

Make g the subject in (2)

$4g + 5h = 28$

$4g = 28 - 5h$

Divide both sides by 4

$g = \frac{1}{4}(28 - 5h)$

Substitute $\frac{1}{4}(28 - 5h)$ for g in (1)

$7g + 3h = 26$

$7(\frac{1}{4}(28 - 5h)) + 3h = 26$

$\frac{7}{4}(28 - 5h) + 3h = 26$

Multiply through by 4

$4 * \frac{7}{4}(28 - 5h) + 4*3h = 26*4$

$7(28 - 5h) + 4*3h = 26*4$

Open bracket

$196 - 35h + 12h = 104$

$196 -23h = 104$

Collect Like Terms

$-23h = 104-196$

$-23h = -92$

Make h the subject

$h = \frac{-92}{-23}$

$h = \frac{92}{23}$

$h = 4$

Substitute 4 for h in $g = \frac{1}{4}(28 - 5h)$

$g = \frac{1}{4}(28 - 5*4)$

$g = \frac{1}{4}(28 - 20)$

$g = \frac{1}{4}(8)$

$g = 2$

This implies that:

1 goldfish = $2

1 hermit crab = $4

The cost of 6 goldfish and 4 hermit crabs is:

$Cost = 6g + 4h$

$Cost = 6*\$2 + 4*\$4$

$Cost = \$12 + \$16$

$Cost = \$28$

5 0

3 years ago

Find the value of x that will make A||B.<br> 5x + 9<br> A<br> B<br> 6x-2<br> X =<br> [?]<br> Enter

givi [52]

Answer:

$x = 11$

Step-by-step explanation:

Given

Parallel lines A and B

Required

Find x

For A and B to be parallel, then 5x + 9 and 6x - 2 are alternate interior angles

And alternate interior angles are always equal

This means that

$5x + 9 = 6x - 2$

Collect like terms

$5x - 6x = -2 -9$

$-x = -11$

Multiply both sides by -1

$-1 * -x = -11 * -1$

$x = 11$

4 0

3 years ago

Read 2 more answers

Gina is a certain age (g). Gina's older sister is twice Gina's age. Gina's brother is half Gina's age. The sum of their ages is

aliina [53]

Answer:

Gina is 12 years old

Step-by-step explanation:

First, we will have to write these statements mathematically and then solve.

Let Gina's age be x, let Gina's brother's age be y and let Gina's sister's age be z.

The second statement"Gina's older sister is twice Gina's age" can be mathematically written as: z =2 x ---------------------------(1)

The next statement "Gina's brother is half Gina's age" can be mathematically written as y = $\frac{x}{2}$ ---------------------------------------(2)

Then the next statement "the sum of their ages is 42" can be mathematically written as: x + y + z = 42 ----------------------------(3)

We can now proceed to solve;

Substitute equation (1) and equation(2) into equation (3)

x + y + z = 42

x + $\frac{x}{2}$ + 2x = 42

Multiply through by 2

2x + x + 4x = 84

7x = 84

Divide both-side of the equation by 7

$\frac{7x}{7}$ = $\frac{84}{7}$

x = 12

Therefore, Gina is 12 years old

7 0

3 years ago