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3 years ago

Which statement best describes g(x) = 3x + 6 - 8 and the parent function f(x) = } ?

Mathematics

1 answer:

kumpel [21]3 years ago

3 0

Answer:

In general gf(x) is not equal to fg(x)

Some pairs of functions cannot be composed. Some pairs of functions can be composed only for certain values of x.

Only with they can be composed some values of x are the ranges of g(x) and f(x) are the same, and their domains are also the same. Or else lies inside it.

Step-by-step explanation:

g(x) = 3x + 6 - 8, f(x) = √x.

The domain of a composed function is either the same as the domain of the first function, or else lies inside it

The range of a composed function is either the same as the range of the second function, or else lies inside it.

Or vice versa

Now only positive numbers, or zero, have real square roots. So g is defined only for numbers

greater than or equal to zero. Therefore g(f(x)) can have a value only if f(x) is greater than or

equal to zero. You can work out that

f(x) ≥ 0 only when x ≥3/2

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Describe the expression using an appropriate term or phrase.

Lena [83]

Answer:

2. the sum of 2 terms

Step-by-step explanation:

It is the sum of 2 terms because in this expression you are simply just adding.

3 0

2 years ago

7. Are the ordered pairs below an arithmetic sequence or geometric

DochEvi [55]

Answer:

8. Arithmetic Progression

9. $f(9) = 300$

Step-by-step explanation:

Given

$\{(1,55)\ (2, 45)\ (3, 35)\ (4, 25)\}$

Solving (8): Arithmetic or Geometric

We start by checking if it is arithmetic by checking for common difference (d).

$d = y_2 - y_1 = y_3 - y_2 = y_4 - y_3$

This gives:

$d = 45 - 55 = 35 - 45 = 25 - 35$

$d = -10 = -10 = -10$

$d=-10$

<em>Because the common difference is equal, then it is an arithmetic progression</em>

Solving (8):

$f(n) = f(1) + f(n-1)$

To find f(9), we substitute 9 for n

$f(9) = f(1) + f(9-1)$

$f(9) = f(1) + f(8)$

We need to solve for f(8); substitute 8 for n

$f(8) = f(1) + f(8 - 1)$

$f(8) = f(1) + f(7)$

We need to solve for f(7); substitute 7 for n

$f(7) = f(1) + f(7 - 1)$

$f(7) = f(1) + f(6)$

We need to solve for f(6); substitute 6 for n

$f(6) = f(1) + f(6 - 1)$

$f(6) = f(1) + f(5)$

We need to solve for f(5); substitute 6 for n

$f(5) = f(1) + f(5 - 1)$

$f(5) = f(1) + f(4)$

From the function, f(4) = 25 and f(1) = 55.

So:

$f(5)=55 + 25$

$f(5)=80$

$f(6) = f(1) + f(5)$

$f(6) = 55 + 80$

$f(6) = 135$

$f(7) = f(1) + f(6)$

$f(7) = 55 + 135$

$f(7) = 190$

$f(8) = f(1) + f(7)$

$f(8) = 55 + 190$

$f(8) = 245$

$f(9) = f(1) + f(8)$

$f(9) = 55 + 245$

$f(9) = 300$

8 0

3 years ago

How many times greater is 1 than 1/4

melisa1 [442]

1 is 4 times greater than 1/4

If you multiply 1/4 by 4 you get 1

4 0

3 years ago

A group of friends had 28 driveways to shovel. If one of them shoveled 1/4 of the driveways, how many driveways did he shovel.

serg [7]

Answer: 7

Step-by-step explanation:

Since we are given the information that a group of friends had 28 driveways to shovel and that one of them shoveled 1/4 of the driveways.

The number of driveways that he shovel will be:

= 1/4 × 28

= 7

Therefore, he shovel 7 driveways.

3 0

3 years ago

For A = {a,b}, determine A x P(A).

alex41 [277]

Answer:

Since A={a,b}, then $P(A)=\{\emptyset, \{a,b\}, \{a\}, \{b\}\}$ . Remember that the Cartesian Product of two sets A, B is defined by

$A\times B=\{(x,y): x\in A \text{ and } y\in B\}$ . Then

$A\times P(A)=\{(a,\emptyset),(a,\{a,b\}),(a,\{a\}), (a,\{b\}), (b,\emptyset),(b,\{a,b\}),(b,\{a\}), (b,\{b\})\}$

6 0

3 years ago