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
Crazy boy [7]
3 years ago
6

Which equation is the inverse of y = 100 – x2?

Mathematics
2 answers:
yulyashka [42]3 years ago
7 0

Answer:

The function f be described by

The graph of this function, is the graph of the parent function , which is the parabola with vertex at (0, 0) which opes upwards:

i) reflected with respect to the y-axis, because of the minus

ii) shifted 100 units up

check the picture attached.

A function has an inverse only if it is decreasing or increasing.

So we must divide the following cases for which the inverses exist:

i)  with domain (-infinity, 0]

ii)  with domain [0, infinity)

To find the formula for the inverse function g of f, we use the property:

f(g(x))=x

thus,

so each of - and + cases, are the inverses of

i)  with domain (-infinity, 0]

ii)  with domain [0, infinity)

At this point, recall that the domain of a function, is the range of it's inverse function,

and the range of the function, is the domain of the inverse function.

thus,

the range of , which is [0,infinity) is the domain of

i)  with domain [0,infinity)

So our answer is:

inverse of i)  with domain (-infinity, 0] is

and the inverse of ii)  with domain [0, infinity) is

Step-by-step explanation:

aleksandr82 [10.1K]3 years ago
4 0
The function f be described by y=100- x^{2}

The graph of this function, is the graph of the parent function x^{2}, which is the parabola with vertex at (0, 0) which opes upwards:

i) reflected with respect to the y-axis, because of the minus

ii) shifted 100 units up

check the picture attached. 


A function has an inverse only if it is decreasing or increasing.


So we must divide the following cases for which the inverses exist:

i) y=100- x^{2} with domain (-infinity, 0]

ii) y=100- x^{2} with domain [0, infinity)


To find the formula for the inverse function g of f, we use the property:

f(g(x))=x

thus, 

f(g(x))=x\\\\ 100-[g(x)]^2=x\\\\g^2(x)=100-x\\\\g(x)= \mp\sqrt{100-x}



so each of - and + cases, are the inverses of 


i) y=100- x^{2} with domain (-infinity, 0]

ii) y=100- x^{2} with domain [0, infinity)


At this point, recall that the domain of a function, is the range of it's inverse function, 

and the range of the function, is the domain of the inverse function.

thus, 

the range of \sqrt{100-x}, which is [0,infinity) is the domain of 

i) y=100- x^{2} with domain [0,infinity)



So our answer is:

inverse of i) y=100- x^{2} with domain (-infinity, 0] is -\sqrt{100-x}


and the inverse of ii) y=100- x^{2} with domain [0, infinity) is 

\sqrt{100-x}

You might be interested in
shoe sells for a certain company were $25.9 billion. sales are expected to increase by about 20% in the next year. find the proj
ExtremeBDS [4]
25.9 × 1.2 = 31.08

$31.08 billion
3 0
3 years ago
If f(x) = 2x -­ 4 and g(x) = x^2+3, find each value.<br><br> 19. (f -­ g)(x)<br> 20. (f • g)(x)
just olya [345]

Step-by-step explanation:

(f - g)(x) = f(x) - g(x) \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: = (2x - 4) - ( {x}^{2}  + 3) \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: = 2x - 4 -  {x}^{2}  - 3 \\     \red{ \boxed{\therefore (f - g)(x)  =  -  {x}^{2}  + 2x - 7}}

5 0
3 years ago
Please help on this problem
lubasha [3.4K]
-6 is the answer since 6*-1 is -6
4 0
3 years ago
(I don't have much points so I can't provide you with a huge amount but I do need help. I do also need the step by step definiti
cluponka [151]

Answer:

this is my answer

Step-by-step explanation:

The expression P(−1.33<z<1.59) represents the area under the standard normal curve above a given value oz. Use your standard normal table to find the indicated area. Use a sketch of the standard normal curve with the appropriate area shaded to help find the answer.What is the value of P(−1.33<z<1.59) between the given values oz?Express your answer rounded to 4 decimal places.The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 100.Sofia scored 632 on the test.What percent of students scored below Sofia?Round your answer to the nearest hundredth.The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 100.Benita scored 432 on the test.What percent of students scored below Benita?Round your answer to the nearest hundredth.The expression P(z<1.00) represents the area under the standard normal curve below a given value oz. Use your standard normal table to find the indicated area. Use a sketch of the standard normal curve with the appropriate area shaded so this is going to let you find the answer.

5 0
3 years ago
Melissa needs to wrap a gift box that is shaped like a rectangular prism. The length is 6 inches, the width is 6 inches and the
vekshin1

Answer:

A=264

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • How do you find the distance of two points on a graph
    8·2 answers
  • Algebra 2 help? Will give brainliest
    6·1 answer
  • Help PLEASE im stucckkkk!!!
    9·1 answer
  • A fish swins 12 miles upstream in 4 hours. The return trip only takes 3 hours. Find the rate of the current
    7·1 answer
  • Find the measure indicated. Assume that the lines which appear to be tangent are tangent. PART 3
    9·1 answer
  • Trthhhhjvbbjjjjj<br>Ghhhhhjjjbn
    12·1 answer
  • How many factors does (2x+5) have
    7·1 answer
  • Find the GCF of 20m and 45.​
    10·2 answers
  • A class is putting ornaments on a Christmas tree.
    9·1 answer
  • ?? math-domain and range
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!