Ask question

Ask question

All categories

andreev551 [17]

3 years ago

5

Let f(x)=9−8x‾‾‾‾‾‾√ .Which of the following decompositions of f(x)=p(q(x)) into a pair of functions p(x) (the outside function)

and q(x) (the inside function) is/are correct ? Select all that apply if more than one is appropriate. A. p(x)=−6x‾‾‾‾√ and q(x)=9+x
B. p(x)=9+x‾‾‾‾‾√ and q(x)=6x
C. p(x)=−x‾‾‾√ and q(x)=6x−9
D. p(x)=9−x‾‾‾‾‾√ and q(x)=6x
E. p(x)=x√ and q(x)=9−6x
F. p(x)=9−6x and q(x)=x√
G. All of the above
H. None of the above

1 answer:

zvonat [6]3 years ago

8 0

Answer:

C, D and E

Step-by-step explanation:

Assuming

f(x) = √(9−8x)

and the options are:

A. p(x) = √(-8x) and q(x)=9+x

B. p(x) = √(9+x) and q(x)=8x

C. p(x) = √(-x) and q(x)=8x−9

D. p(x)=√(9−x) and q(x)=8x

E. p(x)=√x and q(x)=9−8x

F. p(x)=9−8x and q(x)=√x

G. All of the above

H. None of the above

Substituting in f(x)=p(q(x)) we get:

A. √(-8(9+x)) = √(-72 - 8x)

B. √(9+(8x)) = √(9+8x)

C. √(-(8x−9 )) = √(-8x + 9)

D. √(9−(8x)) = √(9−8x)

E. √(9−8x )

F. 9−8(√x ) = 9 - 8√x

You might be interested in

Sanjay graphs a quadratic function that has x-intercepts of –3 and 7. Which functions could he have graphed?

kykrilka [37]

we will select each options and find zeros

(a)

$g(x)=x^2-4x-21$

for finding x-intercept , we can set g(x)=0

and then we can solve for x

$g(x)=x^2-4x-21=0$

now, we can factor it

$(x-7)(x+3)=0$

we get

$x=7,x=-3$

so, this is TRUE

(b)

$g(x)=(x-3)(x+7)$

we can set it to 0

and then we can solve for x

$g(x)=(x-3)(x+7)=0$

we get

$x=3,x=-7$

so, this is FALSE

(c)

$g(x)=3x^2-12x-63$

we can set it to 0

and then we can solve for x

$g(x)=3x^2-12x-63 =0$

$3(x^2-4x-21) =0$

$3(x-7)(x+3) =0$

$x=-3,x=7$

so, this is TRUE

(d)

$g(x)=-(x+3)(x-7)$

now, we can set it to 0

and then we can solve for x

$g(x)=-(x+3)(x-7)=0$

$x=-3,x=7$

so, this is TRUE

(e)

we have

$g(x)=x^2+4x-21$

now, we can set it to 0

and then we can solve for x

$g(x)=x^2+4x-21=0$

$(x+7)(x-3)=0$

$x=-7,x=3$

so, this is FALSE

5 0

3 years ago

Read 2 more answers

Suppose you invest $1400 at interest rate of 4.3% compounded continuously. How much will you have in the account after 7 years?

STatiana [176]

$\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1400\\ r=rate\to 4.3\%\to \frac{4.3}{100}\dotfill &0.043\\ t=years\dotfill &7 \end{cases} \\\\\\ A=1400e^{0.043\cdot 7}\implies A=1400e^{0.301}\implies A\approx 1891.69\implies \stackrel{\textit{rounded up}}{A=1892}$

3 0

3 years ago

What is a formula for the nth term of the given sequence?

lakkis [162]

Answer: option D is the correct answer.

Step-by-step explanation:

The given sequence is a geometric sequence because the consecutive terms differ by a common ratio.

The formula for determining the nth term of a geometric progression is expressed as

an = a1r^(n - 1)

Where

a1 represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a1 = 36

r = 12/36 = 4/12 = 1/3

Therefore, the formula for the nth term of the sequence is

an = 36 × 1/3^(n - 1)

an = 36 × 3^-1(n - 1)

an = 36 × 3^(-n + 1)

an = 36 × 3^(1 - n)

6 0

3 years ago

If a function is written in slope intercept form, y=mx+b, the x represents the ______.

Hitman42 [59]

The x in y = mx + b represents the input, C.

4 0

4 years ago

What is 5 with eponenet of 2

kondaur [170]

Answer:

2^5 =32

25=2x2x2x2x2

=32

Step-by-step explanation:

this is your answer plz let me knowif you got it right in plz rate me the most brainlest

7 0

3 years ago