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
inna [77]
3 years ago
11

Find the inverse of the given function.

Mathematics
2 answers:
kodGreya [7K]3 years ago
7 0

For this case we must find the inverse of the following function:

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

We follow the steps below:

Replace f(x) with y:

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

We exchange the variables:

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

We solve for "y":

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

Multiply by -2 on both sides of the equation:

\sqrt {y + 3} = - 2x

We raise both sides of the equation to the square to eliminate the radical:

(\sqrt {y + 3}) ^ 2 = (- 2x) ^ 2\\y + 3 = 4x ^ 2

We subtract 3 from both sides of the equation:

y = 4x ^ 2-3

We change y by f ^ {- 1} (x):

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

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

OLga [1]3 years ago
5 0

Answer:

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

Step-by-step explanation:

Given : f(x) =-\frac{1}{2}\sqrt{x+3}.

To find : Find the inverse of the given function.

Solution : We have given

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

Step 1: take f(x) = y

y =-\frac{1}{2}\sqrt{x+3}.

Step 2 : Inter change y and x.

x =-\frac{1}{2}\sqrt{y+3}.

Step 3 : Solve for y

Taking square both sides

x^{2} = \frac{1}{4}(y+3).

On multiply both sides by 4.

4x^{2} = (y+3).

On subtraction both sides by 3.

4x^{2} -3 = y.

Here, f(x)^{-1}= y is inverse of f(x)

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

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

You might be interested in
<img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20%5C%200%7D%20%5Cfrac%7B%5Csqrt%7Bcos2x%7D-%5Csqrt%5B3%5D%7Bcos3x%7D%20%7D%7
salantis [7]

Answer:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{1}{2}

General Formulas and Concepts:

<u>Calculus</u>

Limits

Limit Rule [Variable Direct Substitution]:                                                                     \displaystyle \lim_{x \to c} x = c

L'Hopital's Rule

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                    \displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Step-by-step explanation:

We are given the limit:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)}

When we directly plug in <em>x</em> = 0, we see that we would have an indeterminate form:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{0}{0}

This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \displaystyle  \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)}

Plugging in <em>x</em> = 0 again, we would get:

\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \frac{0}{0}

Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:

\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)}

Substitute in <em>x</em> = 0 once more:

\displaystyle \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)} = \frac{1}{2}

And we have our final answer.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

6 0
3 years ago
Please help! Giving brainliest if you include explanation bc I need to learn this
zhannawk [14.2K]

Answer:

B is the most reasonable answer

Step-by-step explanation:

btw 9% of 578 is 52.02, so it works

7 0
2 years ago
Read 2 more answers
Need help asap! Pls
Stels [109]

Answer:

Step-by-step explanation:

The upper right angle is supplement to 130° and a corresponding angle to (3x + 5)

130 + (3x + 5) = 180

3x + 5 = 50

3x = 45

x = 15

8 0
2 years ago
What is the simplified form of the quantity of x plus 3, all over 4 + the quantity of x plus 2, all over 4 ? (2 points) the quan
pentagon [3]
ANSWER

\frac{2x + 5}{4}

EXPLANATION

We want to simplify

\frac{x + 3}{4} + \frac{x + 2}{4}

The fractions have the same denominator so we write one denominator and add the numerators to obtain,

\frac{x + 3 + x + 2}{4}

Regroup in the denominator to get,

\frac{x + x + 3 + 2}{4}

This simplifies to;

\frac{2x + 5}{4}
8 0
3 years ago
When drawn in standard position, in which quadrant does the terminal side of the angle −240° lie?
valina [46]

Answer:

Option (2)

Step-by-step explanation:

All angles are positive when measured counterclockwise from the x-axis.

Terminal side of 240° degrees when measures counterclockwise will lie in the 3rd quadrant.

But the angle is -240°.

That means angle is being measured clockwise from the x-axis.

Therefore, terminal side of the of the angle will be in the 2nd quadrant.

Option (2) will be the correct option.

3 0
2 years ago
Other questions:
  • Graph y= 2x-2 with the domain (1,2,3)
    11·1 answer
  • Geometry pls help !!! Find the value of AB.<br> AB = [?]
    5·1 answer
  • During soccer practice, Alexis tries to score a goal 3 times. For each attempt, the coach writes either G (goal) or N (no goal).
    9·2 answers
  • AB and BC are tangents to P. what is the value of x? this is really so confusing
    11·1 answer
  • Help pls D; I’ll mark brainliest :D
    7·1 answer
  • What is the area of a circle with a radius of 21 cm?
    8·2 answers
  • What are two other ways to name plane C?
    8·1 answer
  • I need help with finding the circumference of a circle.
    11·2 answers
  • What is the zero of f ?
    14·1 answer
  • Use the function f(x) to answer the questions.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!