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
butalik [34]
3 years ago
9

What is the range of the equation

Mathematics
1 answer:
a_sh-v [17]3 years ago
7 0

The range of the equation is y>2

Explanation:

The given equation is y=2(4)^{x+3}+2

We need to determine the range of the equation.

<u>Range:</u>

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

y=2 \cdot 4^{x+3}+2

This can be written as y=2^{1+2(x+3)}+2

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

x=2^{1+2(y+3)}+2

Solving for y, we get;

x-2=2^{1+2(y+3)}

Applying the log rule, if f(x) = g(x) then \ln (f(x))=\ln (g(x)), then, we get;

\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)

Simplifying, we get;

(1+2(y+3)) \ln (2)=\ln (x-2)

Dividing both sides by \ln (2), we have;

2 y+7=\frac{\ln (x-2)}{\ln (2)}

Subtracting 7 from both sides of the equation, we have;

2 y=\frac{\ln (x-2)}{\ln (2)}-7

Dividing both sides by 2, we get;

y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}

Let us find the positive values for logs.

Thus, we have,;

x-2>0

     x>2

The function domain is x>2

By combining the intervals, the range becomes y>2

Hence, the range of the equation is y>2

You might be interested in
Express 0.70330.70330, point, 7033 as a fraction.
lisov135 [29]

Answer:

7033 / 10 000

Step-by-step explanation:

x = .70330

10 000 x = 7033.0   divide both sides by 10 000

x = 7033 / 10 000

6 0
2 years ago
What triangle does it form ?
diamong [38]

Answer:

Scalene triangle

Step-by-step explanation:

A scalene triangle is a triangle with three different side lengths and angle measures. Since none of the side lengths are the same length, then none of the angle measures are the same either leading the correct answer to be scalene.

6 0
3 years ago
Read 2 more answers
All real numbers between negative 5 and 7
Deffense [45]
I hope this helps you -4,-3,-2,-1,0,1,2,3,4,5,6
5 0
3 years ago
Read 2 more answers
What is the area of the square below?
maria [59]

Answer:

Step-by-step explanation:

32

4 0
2 years ago
Read 2 more answers
A square has an area of 561.69m2. Work out the perimeter of the square.
lara [203]

Answer:

The answer is 94.8 m

Step-by-step explanation:

Area of a square is a²

So, 23.7² = 561.69 m²

The side of the square is equal to 23.7 m

Perimeter of a square is the side multiplied by 4

So we have that 23.7 x 4 = 94.8 m

4 0
3 years ago
Other questions:
  • a 4 by 5 inch photo is enlarged by multiplying every dimension by 2 to form a similar 8 by 10 inch photo. What is the ratio of t
    9·1 answer
  • Help pls 2,4 +0,8=........+1,21=........+1,78=........-5,14=
    6·1 answer
  • Find the area of a triangle with base 8 and height 17
    6·2 answers
  • Please help me i have inly minutes left​
    12·1 answer
  • 7+5+3+... + (-287) =
    8·2 answers
  • Ms Etienne deposited $450 into an account to pay 5% interest compounded annually she did not make any additional deposits or wit
    7·2 answers
  • How do you write 60% as a decimal?​
    8·2 answers
  • 5.
    11·1 answer
  • Graph the inequality.<br> 2x+5y&gt; -15
    13·2 answers
  • X+6y=28, solve for y
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!