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
Stolb23 [73]
3 years ago
10

F(x) = x2 - 4. Find the inverse of the function

Mathematics
1 answer:
Lisa [10]3 years ago
5 0

Answer:

f^{-1}(x) = √ x + 4

Step-by-step explanation:

step 1) replace f(x) with y

y = x² - 4

step 2) switch the x and y (because every (x, y) has a (y, x))

x = y² - 4

step 3) add 4 to both sides of the equal sign

x + 4 = y²

step 4) take the square root of both sides of the equal sign (the square root symbol cancels out the ²)

√ x + 4 = y

step 5) you know have the inverse of f(x) = x² - 4

f^{-1}(x) = √ x + 4

You might be interested in
Consider the rational number 3/11 a. What are the value of a and b in a divide by b when you use division to find the decimal fo
PolarNik [594]

Answer:

The decimal form of this rational number is 0.\overline {27}.

Step-by-step explanation:

a) Let \frac{a}{b} a rational number. From statement we understand that a represents the numerator, while b corresponds with the denominator of the rational number. Hence, a is 3 and b is 11.

b) The decimal form is obtained by dividing a by b, we presented the step needed to determine the decimal form:

i) Multiply the numerator by 10:

Dividend: 30/Divisor: 11/Known result: 0. /Residue: N/A

ii) Multiply the divisor by 2 and subtract from the dividend:

Known result: 0.2 /Residue: 8

iii) Multiply the residue by 10:

Known result: 0.2 /Residue: 80

iv) Multiply the divisor by 7 and subtract from the residue:

Known result: 0.27 /Residue: 3

v) Multiply the residue by 10:

Known result: 0.27 /Residue: 30

vi) Multiply the divisor by 2 and subtract from the residue:

Known result: 0.272/Residue: 8

vii) Multiply the residue by 10:

Known result: 0.272 /Residue: 80

viii) Multiply the divisor by 7 and subtract from the residue:

Known result: 0.2727/Residue: 3

We have notice that the decimal form of \frac{3}{11} is a periodical decimal number. Hence, we conclude that decimal form of this rational number is 0.\overline {27}.

3 0
2 years ago
The quantity, Q, of a drug in the blood stream begins with 250 mg and decays to one-fifth its value over every 90 minute period.
Mazyrski [523]

Answer:

a=250 \, mg\\\\b=5\\\\T= 90'

Step-by-step explanation:

We have that Q(t) = a\cdot b^{-\frac{t}{T}} \\

Where t is the time (in minutes) and for the sake of dimensional consistency, let's assume that T is also in minutes, b is an adimensional number, and a is in mg.  So we will have Q in mg as a consequence.

We now want to find out what values these constants might take. Let's see what happens when t=0, that is, just as we start. At that point, we have that the amount of drug in the bloodstream must be equal to 250mg, thus:

Q(0)= a\cdot b ^{-\frac{0}{T} }=250\,mg\\Q(0)= a=250\,mg

We have found the constant a! It is the initial amount of drug! we have made use of the fact that any number raised to the 0th power is equal to one.

Now, we know that every 90 minutes, the amount of drug decreases to one fifth of its former value. How do we put this in mathematical form? Like so:

Q(t+90')=Q(t)/5

That is, 90 minutes after time t the amount of drug will be one fifth of the amount of drug at time t. Let's expand the last equation:

Q(t+90')=Q(t)/5\\\\a\cdot b^{-\frac{t+90'}{T} }=a\cdot b^{-\frac{t}{T} }/5\\\\ b^{-\frac{t+90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{t}{T} }b^{-\frac{90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{90'}{T} }=\frac{1}{5}

Now the last expression isn't enough to determine both T and b, but that also means that we have some freedom in how we choose them. What seems most simple is to pick T=90' and thus we will get:

b^{-1 }=\frac{1}{5}\\\\\frac{1}{b}= \frac{1}{5}\\\\b=5

And that is our final result.

3 0
3 years ago
A triangle has three sides 35cm 54 cm and 61 cm find its area Also find the smallest of its altitude ​
I am Lyosha [343]

Answer:

Area of given triangle is 939.15cm² and smallest altitude is 30.8cm

<h3>Solution:</h3>

We are given three sides of a triangle, Let the sides be :

  • ( a ) = 35 cm

  • ( b ) = 54 cm

  • ( c ) = 61 cm

We can find the area of the triangle with its three sides using Heron's Formula

  • <u>Heron's </u><u>Formula</u>

Heron's formula was founded by hero of Alexandria, for finding the area of triangle in terms of the length of its sides. Heron's formula can be written as:

\sf{   \pmb { \longrightarrow \:  \sqrt{s(s - a)(s - b)(s - c)} }}

where ( s ) :

\sf \longrightarrow s = \dfrac{a + b + c}{2}

Therefore, for the given triangle first we will calculate ( s )

\begin {aligned}\quad & \quad \longmapsto  \sf  s =  \dfrac{a + b + c}{2}  \\  & \quad \longmapsto  \sf s =  \dfrac{35 + 54 + 61}{2}  \\ & \quad \longmapsto  \sf s =  \dfrac{150}{2}  \\ & \quad \longmapsto  \sf s  = 75cm \end{aligned}

Now, Area of triangle will be:

\begin{aligned}&:\implies \sf\quad \sf \:  A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \:  A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)}   \\&:\implies \sf\quad \sf \:  A = \sqrt{75 \times 40 \times 21 \times 14}  \\ &:\implies \sf\quad \sf \:  A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5}  \\ &:\implies \sf\quad \sf \:  A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5}  \\ &:\implies \sf\quad \sf \:  A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf   A =939.15 {cm}^{2} }} \end{aligned}

Also, we have to find the smallest altitude, and the smallest altitude will be on the longest side. So,

\begin{aligned}&:\implies \sf\quad \sf \:  Area =939.15 \\ &:\implies \sf\quad \sf \:   \dfrac{1}{2}  \times b \times h =939.15 \\ &:\implies \sf\quad \sf \:   \dfrac{1}{2} \times 61 \times h  = 939.15 \\&:\implies \sf\quad \sf \:  h =939.15 \times  \dfrac{2}{61}   \\&:\implies \sf\quad \sf \:  h = \dfrac{1818.3}{61}  \\ &:\implies \sf\quad  \boxed{ \pmb{\sf \:  h =30.79 \: (approx)}} \end{aligned}

3 0
2 years ago
Read 2 more answers
PLEASE HELPPPP, Graph the equations using slope intercept form. y = -3x + 8
Zolol [24]

Answer:

Slope = -3

y- intercept= (0,8)

x : 0, 8/3

y : 8, 0

8 0
3 years ago
What is the rate of change of the function?
Dominik [7]
I think it would be -3
5 0
3 years ago
Other questions:
  • 50. Two airplanes leave the airport at the same time, flying in opposite directions. One plane flies 100 miles per hour faster t
    9·2 answers
  • What is the integral of <br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B1%20%2B%203x%7D%20" id="TexFormula1" title=" \
    5·1 answer
  • A bicycle is traveling at 17 mph. How many feet will it cover in 50 seconds?
    8·2 answers
  • What is the multiplicative inverse of 10 upon -2
    5·1 answer
  • Edith is balancing her lawn care business' check registry. Her initial balance was $5,850.25. She deposited a check for $45.00 a
    9·2 answers
  • Solve for X : 2X² + 2/5 = 12/5. *
    8·1 answer
  • Can you help me solve this?<br> Thanks!
    5·1 answer
  • What two numbers multiply to 11 and add to -12
    5·2 answers
  • Does the point (5 6) satisfy the equation y = 2x - 7
    13·1 answer
  • Which of the following choices is equivalent to -9x &gt; -27?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!