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
vodka [1.7K]
3 years ago
12

F(x)=

middle" class="latex-formula">, x\leq \}0
find (f^-^1)'(1)


I keep getting the wrong answer. The correct answer is\frac{1}{\sqrt{5} }
Mathematics
1 answer:
hammer [34]3 years ago
3 0

Solve for <em>x</em> when √(<em>x</em> ² - 4) = 1 :

√(<em>x</em> ² - 4) = 1

<em>x</em> ² - 4 = 1

<em>x</em> ² = 5

<em>x</em> = ±√5

We're looking at <em>x </em>≤ 0, so we take the negative square root, <em>x</em> = -√5.

This means <em>f</em> (-√5) = 1, or in terms of the inverse of <em>f</em>, we have <em>f</em> ⁻¹(1) = -√5.

Now apply the inverse function theorem:

If <em>f(a)</em> = <em>b</em>, then  (<em>f</em> ⁻¹)'(<em>b</em>) = 1 / <em>f '(a)</em>.

We have

<em>f(x)</em> = √(<em>x</em> ² - 4)   →   <em>f '(x)</em> = <em>x</em> / √(<em>x</em> ² - 4)

So if <em>a</em> = -√5 and <em>b</em> = 1, we get

(<em>f</em> ⁻¹)'(1) = 1 / <em>f '</em> (-√5)

(<em>f</em> ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5

The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of <em>f</em> at <em>x</em> = 1.

You might be interested in
Solve each equation? (n+2) ( n+1)= 0
Delicious77 [7]

Answer:

n=-2,\:n=-1

Step-by-step explanation:

\left(n+2\right)\left(n+1\right)=0\\\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\\\mathrm{Solve\:}\:n+2=0:\quad n=-2\\n+2=0\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\n+2-2=0-2\\\mathrm{Simplify}\\n=-2\\\mathrm{Solve\:}\:n+1=0:\quad n=-1\\n+1=0\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\n+1-1=0-1\\Simplify\\n=-1\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\n=-2,\:n=-1

7 0
3 years ago
Read 2 more answers
PLZ HELP!
Rama09 [41]

Answer:

C i am pretty sure

Step-by-step explanation:

4 0
2 years ago
David measures how many inches his tomato plant grows every week. What is the independent variable?​
Norma-Jean [14]

Answer:

It is tomato plant

Step-by-step explanation:

- The independent variable is the variable the experimenter changes or controls and is assumed to have a direct effect on the dependent variable. - - - The dependent variable is the variable being tested and measured in an experiment, and is 'dependent' on the independent variable.

7 0
3 years ago
Tina practiced piano for 15 hours last month and 45 hours this month. Use multiplication to write a statement comparing the hour
Pani-rosa [81]

Answer: Hours by Tina practiced this month is 3 times the hours she practiced last month such that 15 x 3 =45 hours.


Step-by-step explanation:

Given : Duration of Tina practiced piano last month=  15 hours

Duration of Tina practiced piano this month=  45 hours

We can see 45 is a multiple of 15 such that 45=15\times3

Therefore, Hours by Tina practiced this month is 3 times the hours she practiced last month such that 15 x 3= 45 hours.

6 0
3 years ago
Read 2 more answers
What is 23/46 reduced
artcher [175]
If you were trying to simplify it, it's not posible because 23 is a composite number so I just went ahead and did division for you:
23/46=0.5
I hope this helped!
4 0
3 years ago
Read 2 more answers
Other questions:
  • Find the area of the polygon defined by the coordinates (0, -5), (-5, 0), (-15, -20), and (-20, -15). A) 90 square units B) 110
    9·2 answers
  • What is the probability of rolling a number greater than or equal to 8 with the sum of two dice given that at least one of the d
    10·2 answers
  • When i was two, my brother was half my age<br> now i am 100. what is my brothers age
    5·2 answers
  • The rectangle below has an area of 121-x^2121−x
    9·1 answer
  • 1) Give an example of a math formula.
    6·1 answer
  • What is the gcf of 42 and 60​
    6·2 answers
  • 6
    5·1 answer
  • Find two consecutive odd numbers whose sum is 44.
    11·1 answer
  • This app and you guys help me a lot and all need today is thank you and I need help
    11·2 answers
  • Please help I can't understand and my teacher is not explaining properly.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!