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
Scilla [17]
3 years ago
11

Algebra 2!! The equation of the piecewise function f(x) is below. What is the value of f(3)?

Mathematics
1 answer:
VladimirAG [237]3 years ago
3 0

Answer:

5

Step-by-step explanation:

Ask your self which equation you should use. Since it says F(3) then we have to find an equation that would fit this correctly. For example if we look at -X^2, X<-2 we could see that 3 is clearly not less than -2, leading to the conclusion that this is not the right equation.. If you look at the last equation it says that x has to be greater/equal to 0 which is true. So then we are left with the equation...

F(3)=x+2

F(3)=3+2

F(3)=5

You might be interested in
Solve the equation for x:<br> 2(8x – 16) = 48
mihalych1998 [28]
16x-32=48 /+32
16x=80/:16
X=5
3 0
2 years ago
Read 2 more answers
What is Limit of StartFraction StartRoot x + 1 EndRoot minus 2 Over x minus 3 EndFraction as x approaches 3?
scoray [572]

Answer:

<u />\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \boxed{ \frac{1}{4} }

General Formulas and Concepts:

<u>Calculus</u>

Limits

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

Special Limit Rule [L’Hopital’s Rule]:
\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Addition/Subtraction]:
\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]
Derivative Rule [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:

<u>Step 1: Define</u>

<em>Identify given limit</em>.

\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3}

<u>Step 2: Find Limit</u>

Let's start out by <em>directly</em> evaluating the limit:

  1. [Limit] Apply Limit Rule [Variable Direct Substitution]:
    \displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \frac{\sqrt{3 + 1} - 2}{3 - 3}
  2. Evaluate:
    \displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \frac{\sqrt{3 + 1} - 2}{3 - 3} \\& = \frac{0}{0} \leftarrow \\\end{aligned}

When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:

  1. [Limit] Apply Limit Rule [L' Hopital's Rule]:
    \displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\\end{aligned}
  2. [Limit] Differentiate [Derivative Rules and Properties]:
    \displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \leftarrow \\\end{aligned}
  3. [Limit] Apply Limit Rule [Variable Direct Substitution]:
    \displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \leftarrow \\\end{aligned}
  4. Evaluate:
    \displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \\& = \boxed{ \frac{1}{4} } \\\end{aligned}

∴ we have <em>evaluated</em> the given limit.

___

Learn more about limits: brainly.com/question/27807253

Learn more about Calculus: brainly.com/question/27805589

___

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

Unit: Limits

3 0
1 year ago
For his long distance phone service, Ahmad pays a $3 monthly fee plus 11 cents per minute. Last month, Ahmad's long distance bil
Alenkinab [10]

Answer:

198 minutes (3 hours and 18 minutes)

Step-by-step explanation:

24.78 - 3 = 21.78

21.78 ÷ 0.11 = 198

Hope this helped!

Stay safe! <3

3 0
2 years ago
1. Find the distance from point P to QS
12345 [234]

Answer:

5.7 units

Step-by-step explanation:

The distance from point P to QS is the distance from point P (1, 1) to the point of interception R(-3, 5).

Use distance formula to calculate distance between P and R:

PR = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

P (1, 1) = (x_1, y_1)

R(-3, 5) = (x_2, y_2)

Plug in the values into the formula.

PR = \sqrt{(-3 - 1)^2 + (5 - 1)^2}

PR = \sqrt{(-4)^2 + (4)^2}

PR = \sqrt{16 + 16}

PR = \sqrt{32}

PR = 5.7 units (to nearest tenth)

4 0
3 years ago
Perform the following divisions. be sure all answers are reduced to lowest terms. 4/3 ÷ 1/2 =
Kobotan [32]
The answer is 8 divide by 3
7 0
3 years ago
Other questions:
  • Write two numbers that when rounded to the thousands place have an estimated sum of 10,000
    10·1 answer
  • Pls help me i give brainliest
    13·2 answers
  • The radius of a cylinder is measured in meters. What unit will the surface area be measured in?
    10·2 answers
  • What is the slope of the line that is represented by the values in the table above?
    15·1 answer
  • 100 POINTS!!!
    13·1 answer
  • Help please easy 8th grade math!!!❤️❤️❤️❤️❤️❤️❤️❤️❤️The ages of Moe, Larry, and Curly are consecutive odd numbers, where Moe is
    14·1 answer
  • picture above
    15·2 answers
  • Find the area for this problem
    5·1 answer
  • 4/10x - 2x + 8/5 = 4/5
    9·1 answer
  • The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!