1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dovator [93]
2 years ago
11

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Mathematics
2 answers:
GrogVix [38]2 years ago
7 0

Answer:

  1. D. f^-1(x) = log2(x -6)
  2. 4x^2 -3 . . . . x ≤ 0
  3. B. √(x^5) -3√(x^3) -18√x

Step-by-step explanation:

1. When you replace f(x) by x and x by y, you have

... x = 2^y + 6

The first thing you do is subtract 6; then you take the base-2 logarithm:

... (x -6) = 2^y

... log2(x -6) = y = f^-1(x)

You know that to get the y-term by itself, you must subtract 6. Anything else you do will operate on (x-6). Only answer choice D has that sort of construction.

2. When you swap x and y and solve for y, you have ...

... x = -1/2√(y+3)

... -2x = √(y +3) . . . . . . multiply by -2

... (-2x)^2 = y +3 . . . . . square

... 4x^2 - 3 = y = f^-1(x) . . . . subtract 3

The range of f(x) is (-∞, 0], so that is the domain of f^-1(x). That is, f^-1(x) is defined for x ≤ 0.

3. The product of the two functions is ...

... (x -6)(√x)(x +3) = (√x)(x^2 -3x -18)

<em>Every term</em> will have a factor of √x, and the coefficients will be 1, -3, -18. Only selection B matches those conditions.

Leto [7]2 years ago
3 0

Answer:

Question One: log_2(x - 6) = y

Question Two: First blank: 4 Second blank 0

Question Three: B


Step-by-step explanation:

f(x) = 2^x + 6

y = 2^x + 6                 Interchange the x and y

x = 2^y + 6                Subtract 6 from both sides

x - 6 = 2^y                 Take the log of both sides

log(x - 6) = log 2^y    The power can be multiplied by the log of 2

log(x - 6) = y log(2)    Divide by the log of 2

log(x - 6)/log(2) = y    This to me is the preferred answer. It allows you to calculate what the actual number is or graph it on Desmos

The answer I have given is equivalent to using base 2 as your log, but calculating that is not always easy.

log_2(x - 6) = y

Answer: D

Problem Two

You want the inverse of y = - 1/2 sqrt(x + 3)   x ≥ - 3

Note: you cannot have any number less than -3 because if you do, you will be taking the square root of -x which involves complex numbers. In addition x ≥ -3 is a domain. You have to keep that in mind when doing this question.

  • y = - 1/2 sqrt(x + 3)                   Interchange the x and y
  • x = - 1/2 sqrt(y + 3)                   Multiply by - 2
  • -2x = sqrt(y + 3)                       Square both sides
  • (-2x)^2 = sqrt(y + 3)^2                          
  • 4x^2 = y + 3                             Subtract 3 from both sides
  • y = 4x^2 - 3

The domain and range of this is a little harder to figure out. The range of f(x) becomes the domain of f-1(x)

The range of f(x) is 0 <=y < - infinity

So the domain of f-1(x) <= 0

Answer: The first blank is 4 and the second one is 0

Graph: the graph is given you below the question. What it shows is the f(x) and f^-1(x) are symmetrical about y = x. Most inverses are. If you want to check your work, it is best to include a graph when doing inverses.

  • Red Original
  • Blue inverse
  • Black: y = x

Problem Three

The best way to begin this problem is to apply the associative property of multiplication and start by rewriting the givens as x^(1/2)[(x - 6)(x + 3)]. Do what is in the square brackets first.

  • x^(1/2) [x^2 - 6x + 3x - 18]
  • x^(1/2) [x^2 - 3x - 18]              

Now deal with the x^(1/2) which must be multiplied by all three terms in the square brackets.

  • x^(1/2)*x^2: x^(2 + 1/2) = x^(4/2 + 1/2) = x^(5/2)
  • x^(1/2)*(-3x): - 3 x^(2/2 + 1/2) = - 3x^(3/2)
  • x^(1/2)*(-18):  - 18x^(1/2)

Result: x^(5/2) - 3x^(3/2) - 18x^(1/2)

Answer: √(x^5) - 3√x^3 - 18√x

Answer: B

You might be interested in
PLS EXPLAIN IN FULL DETAIL
elena-14-01-66 [18.8K]

Answer:

1.50x=18

x=12

Step-by-step explanation:

You have to divide 1.50 on both sides and 1.50x/1.50= x and 18/1.50=12 so x=12

3 0
2 years ago
Read 2 more answers
Jeri has 2/3 yard of fabric to use for making some puppets she needs 1/6 yard for each puppet how many puppets can jeri make wit
AlekseyPX

Answer:4

Step-by-step explanation:

6 0
2 years ago
What is the numerical sum of angle DEA (X+25) and angle AEB (9x+10) ?
Sonbull [250]
10x + 35
If it is just the sum then it is this.
8 0
3 years ago
Please help me PLEASEE
zaharov [31]

Answer:?????

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Find the area of a circle with a circumference of 6.28 units ​
ad-work [718]

Answer 3.14

Step-by-step explanation:

Area= pi*r^2

Circumference=2*pi*r

Area=C^2/4pi= 6.28^2/4*pi which ='s 3.13841

8 0
2 years ago
Other questions:
  • Which is the correct formula to find the distance between two points (p, q) and (m, n)?
    6·1 answer
  • What is the answer to 8×(11+2)
    7·2 answers
  • Answer the question and I will mark brain also explains why you chose your answer :)
    5·1 answer
  • Solve for y <br> x + 5y = 5
    5·2 answers
  • Write the sentences as proportion. Twelve hundredths is to three as twenty-four hundredths is to eight
    6·1 answer
  • What set of transformations is performed on ABCD to form A′B′C′D′?
    7·1 answer
  • Please help me asap
    8·1 answer
  • What is the perimeter of ^PQR with vertices P(-2,9) Q(7,-3) and R(-2,-3) in the coordinate plane?
    6·1 answer
  • Pls help! 15 points<br> It’s for math
    8·2 answers
  • Find the distance between each pair of points (-6,-5) and (2,0)
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!