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
wolverine [178]
3 years ago
11

[Will mark as brainliest]

Mathematics
1 answer:
Aleks04 [339]3 years ago
4 0

The answer is: f^{-1} = 4x^2-3,\quad\text{for  } x \leq 0

The inverse of a function f(x) is another function, f^{-1}(x), with the following property:

f(f^{-1}(x)) = f^{-1}(f(x)) = x

In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.

Think for example to a function that doubles the input, f(x)=2x, and one that halves it: f(x)= \frac{x}{2}. Their composition is clearly the identity function f(x)=x, since you consider "twice the half of something", or "half the double of something".

In general, to invert a function y=f(x), you have to solve the expression for x, writing an expression like x = g(y). If you manage to do so, then g is the inverse of f.

In your case, you have

f(x) = y = -\frac{1}{2}\sqrt{x+3}

Multiply both sides by -2 to get

-2y = \sqrt{x+3}

Square both sides to get

4y^2 = x+3

Finally, subtract 3 from both sides to get

x = 4y^2 - 3

Since the name of the variables doesn't really have a meaning, you can say that the inverse function is

f^{-1}(x) = 4x^2 - 3

As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain b \in B such that there exists a \in A : f(a)=b. So, we need the range of f(x).

We know that the range of g(x)=\sqrt{x} is [0,\infty). When you transform it to g(x)=\sqrt{x+3} you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times -\frac{1}{2} you affect both extrema of the range, turning it into (-\infty,0], which you can simply write as x \leq 0

You might be interested in
Please help me
stellarik [79]

Answer:1.00

Step-by-step explanation:I misses u

8 0
3 years ago
Read 2 more answers
(20 pts!) if the base of the roof has length 40 feet and x=30, which of the following gives the height of the roof?
musickatia [10]

Answer:

23.094 ft approximately

(If you want your answer in a different format, let me know please.)

Step-by-step explanation:

I would have solve this using tangent since the side opposite to x is asked for and the adjacent side to side is given as having a measurement of 40 ft.

But I think they want you to use the formula:

l=\frac{b}{\cos(x)}.

l=\frac{40}{\cos(30)}

Input into calculator:

l=46.188 (approximation)

l represents the length of the roof.

So we have l=46.188 and b=40.

We must use the Pythagorean Theorem to find the height,h, for of the roof.

l is the hypotenuse.

h^2+40^2=46.188^2

h^2+1600=2133.331

Subtract 1600 on both sides:

h^2=533.331

Take square root of both sides:

h=23.094

The answer is 23.094 feet for the height that roof reaches on the building.

I want to show you another way:

\tan(x)=\frac{\text{opposite}}{\text{adjacent}}

\tan(30)=\frac{h}{40}

Multiply both sides by 40:

40\tan(30)=h

Input into calculator:

23.094=h

I didn't do it this way because your problem suggested you use their formula to find the height.

8 0
3 years ago
Read 2 more answers
The measure of an angle is 131°. What is the measure of its supplementary angle?
sp2606 [1]

Answer:

the supplementary angle to 313 would be 49.

Step-by-step explanation:

the supplement of an angle is when tow angles add up to equal 180 degrees. therefore, if you subtract 131 from 180, you would get the answer of 49 degrees.

5 0
3 years ago
Read 2 more answers
Solve the equation and check your answer. 61 2 = 11 4 + n Which statements are correct? Check all that apply.
Alexandra [31]
Is there anything between the 61 and 2? Or is it supposed to be 612 same thing with 11 and 4
4 0
3 years ago
Read 2 more answers
Simplify the expression (2i-5j)×(3i+4j)​
Alex_Xolod [135]

Answer:

-6-7ji-20j^(2)

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • I need a step by step explanation on this problem:
    14·1 answer
  • Write 12/15 in the simplest form
    5·2 answers
  • Pirate Jack has an equal number of gold and silver coins. If Pirate Jack splits all of his coins into 7 equal piles for his parr
    6·1 answer
  • What is the best order-of-magnitude estimate for 789,000?
    8·1 answer
  • Which fraction is equal to 2/8?
    6·2 answers
  • Simplify the expression. 1−(sec2x−tan2x)
    8·1 answer
  • -5(1 - r) - 2<br> Find r
    7·1 answer
  • . Given that O is the centre of the following circle, find the values of the unknowns.​
    9·1 answer
  • HELPPP PLEASEEEEE
    11·2 answers
  • a researcher found a study relating the distance a driver can see, y, to the age of the driver, x. when researchers looked at th
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!