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
A truck was carrying a load of 458 pounds of gravel. Another 231 pounds of gravel was loaded onto the truck.
Mila [183]

Answer:

A. Olivia is correct.

Step-by-step explanation:

If the total amount of gravel stated is 689 pounds and you want to check your answer, you can subtract one of the two trucks from the total. Which would be either 689 - 231 or 689 - 458. Therefore, A is the correct answer.

6 0
3 years ago
What is thirty-four and twelve hindredths in expanded form?
strojnjashka [21]
The answer is two hundred thirty four.
6 0
3 years ago
Can someone please help me with the bar with missing numbers? Please it’s hard for me
alexandr402 [8]
You multiply the number of cars(bottom row) by 4 to get the number of tires(top row) so if there are 4 cars then there will be 16 tires. If you think about it, there are 4 tires on a car so you would multiply the number of cars by 4 to get the number of tires
4 0
3 years ago
Find the degree of the monomial 7x^7 y^3
KengaRu [80]
I believe the answer is 7 but I’m 99% sure ,
Sorry if it’s incorrect
5 0
3 years ago
Read 2 more answers
Three lights all go on one changes every 5 sec one every 6 sec one every 8 sec when will they all go on together
inysia [295]
In order to calculate, you need to find their LCM
LCM of 5,6 and 8 is equal to 120

So, That time will be 120 sec = 2 min.
In short, Your Final Answer would be 2 min.

Hope this helps!
3 0
3 years ago
Other questions:
  • Sdfghjkljhgfdxzs idk
    15·2 answers
  • What is the quantity 987 milligrams expressed in grams?
    12·2 answers
  • What is the prescribed dosage of a certain medicine for a 6-year-old child if the adult dosage of
    13·1 answer
  • How do u simplify 5x^2-8x-12 subracted from -4x^2+2x-8
    15·1 answer
  • You owe $225 on your credit card. You make a $55 payment and then purchase $87 worth of clothes at Target. What is the integer t
    15·1 answer
  • Your sock drawer contains 5 pairs of 5 white socks, 3 pair of blue socks, 1 pair of striped socks, and 6 pair of red socks. you
    10·1 answer
  • Consider the function y 2x+3. which is true
    6·2 answers
  • Choose the correct simplification of the expression (xyz2)4. X5y5z6 x5y5z8 xyz16 x4y4z8.
    13·1 answer
  • Solve for "y" if 2x + 8y = 6
    6·1 answer
  • Marcel and his 8 friends have a snow shoveling business. Last season, they earned a total of $2,240.64. How much
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!