To find the inverse of a function, switch x and y and solve for y. The inverse of f(x) = (x-1)/5 is f^-1(x) = 5x + 1. Verify that f(f^-1(x)) = x and f^-1(f(x)) = x.
Explanation:To find the inverse of a function, we need to switch the roles of x and y and solve for y. In other words, we need to solve the equation y = (x-1)/5 for x. Let's do that:
Step 1: Replace y with x and x with y: x = (y-1)/5.
Step 2: Solve for y: Multiply both sides by 5: 5x = y - 1. Add 1 to both sides: 5x + 1 = y.
So, the inverse of f(x) = (x-1)/5 is f-1(x) = 5x + 1.
To verify that f(f-1(x)) = x, substitute f-1(x) into f(x) and simplify:
f(f-1(x)) = f(5x + 1) = ((5x + 1) - 1)/5 = 5x/5 = x.
Similarly, to verify that f-1(f(x)) = x, substitute f(x) into f-1(x) and simplify:
f-1(f(x)) = f-1((x-1)/5) = 5((x-1)/5) + 1 = x-1+1 = x.
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Which quantity is used to generate the error bars on a graph?
range
median
linear correlation
standard deviation
Answer:
D
Step-by-step explanation:
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Maggie was thinking of a number. If she multiply the number by 3 ,subtracted by 8 ,added by 2 times the 5 original number . the result was 48. write an equation that the number satisfies. Then answer it.
To solve the word problem, we set up and solved an algebraic equation. Maggie's original number is approximately 4.31 after converting the written problem into the equation 3x - 8 + 10x = 48 and solving for 'x'.
The goal is to translate the word problem into an algebraic equation and solve for the unknown number. If Maggie is thinking of a number, let's use 'x' to represent this unknown number. According to the problem, she multiplies the number by 3, subtracts 8, and then adds 2 times the original number 5 times. The result of these operations is 48. Here's how you set up the equation:
3x - 8 + 10x = 48
The next step is to combine like terms:
13x - 8 = 48
Now we add 8 to both sides of the equation:
13x = 56
The last step is to divide both sides by 13 to solve for x:
x = 56 / 13
x = 4.3077 or approximately 4.31 if rounded to two decimal places.
Therefore, Maggie's number is approximately 4.31.
Use the graph below for this question:
graph of parabola going through 0, 3 and 2, negative 5.
What is the average rate of change from x = 0 to x = 2?
− 4
− 8
1
5
Can you please help me?
The average rate of change from x = 0 to x = 2 for the parabola described in the question is -4. Hence the correct option is 1.
The average rate of change of a function between two points is calculated by subtracting the y-values (function outputs) and dividing by the difference in x-values (inputs). In this case, to find the average rate of change of the parabola from x = 0 to x = 2, we use the points (0, 3) and (2, -5).
The average rate of change = (y2 - y1) / (x2 - x1)
Substitute in the given points: ( -5 - 3 ) / ( 2 - 0 )
Simplify the expression: -8 / 2 = -4
alfonso makes $8 per hour working at movie theater and $12 per hour working at a restaurant. Next week Alfonso is scheduled to work 6 hours at a the movie theater. which of the following inequalities represents the amount of hours (h) that alfonso needs to work at the restaurant next week to earn at least $144 between his two jobs
Use the stem and leaf plot shown to answer the following question.
What is the upper quartile median value?
37
40
41
Answer:
The upper quartile median value is 40. Therefore second option is correct.
Step-by-step explanation:
Stem is first digit of a number and leaf is last digit of a number.
Stem 1 leaf 4 can be written as 14.
From the given table, the observations can be written as
[tex]16,18,23,25,26,34,37,37,40,41,46[/tex]
Total number of observations is 11, which is an odd number.
[tex]median=\frac{n+1}{2}\text{th term}[/tex]
[tex]median=\frac{11+1}{2}\text{th term}=6\text{th term}[/tex]
Therefore median is 34.
We have 5 terms before 34 and 5 terms after 34.
[tex]Q_1=\frac{n+1}{4}\text{th term}=3\text{th term}[/tex]
[tex]Q_1=23[/tex]
[tex]Q_3=\frac{3(n+1)}{4}\text{th term}=9\text{th term}[/tex]
[tex]Q_3=40[/tex]
Q₃ is also known as upper quartile median value. Therefore second option is correct.
If arc AXC = 235°, what is m∠ABC?
117.5°
60°
55°
125°
The measure of the exterior angle of the circle ∠ABC = 55°
What is the Area of the Sector?In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
The formula for Area of a sector is given as;
A = θ/360 x πr²
where;
θ is the central angle of the sector
r is radius
Given data ,
Let the measure of the arc be represented as A = 235°
So , the difference of the measures of arc = 235 - 125°
Now , the measure of the external angle ∠ABC = ( 235 - 125 ) / 2
So , the external angle ∠ABC = 55°
Hence , the measure of angle ∠ABC = 55°
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The distance a spring will stretch varies directly with how much weight is attached to the spring. if a spring stretches 9 inches with 100 pounds attached, how far will it stretch with 90 pounds attached? round to the nearest tenth of an inch.
Clark Kent walks 3 miles west and then 4 miles north. How far is it for Superman to fly in a straight line back to his starting point? (It makes a right triangle.)
What is the greatest common factor of 20, 45x?
Which of the following shows the extraneous solution to the logarithmic equation below?
log3(18x^3)-log3(2x)=log3(144)
x=-16
x=-8
x=-4
x=-2
The value that shows the extraneous solution to the logarithmic equation below is x = -4
Extraneous solutions to a system of equationGiven the logarithmic function expressed as:
log3(18x^3)-log3(2x)=log3(144)
This can also be written as:
log3(18x^3/2x) = log3(144)
log3 (9x^2) -= log3 (144)
Cancel out the log function to have:
9x^2 = 144
Divide both sides by 9
x^2 = 144/9
x^2 = 16
x = ±4
Hence the value that shows the extraneous solution to the logarithmic equation below is x = -4
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rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x) + r(x)/b(x)
To rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x) + r(x)/b(x), we can use polynomial division.
Explanation:To rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x) + r(x)/b(x), we can use polynomial division. Here are the steps:
Divide x^3+5x^2+3x-10 by x+4 using polynomial division.Write the quotient obtained as q(x) and the remainder obtained as r(x).The denominator b(x) is the divisor, which is x+4.Therefore, the rational expression x^3+5x^2+3x-10/x+4 can be rewritten as q(x) + r(x)/b(x), where:
q(x) is the quotient obtained from polynomial division.r(x) is the remainder obtained from polynomial division.b(x) is the divisor, which is x+4.
is it possible for a line to pass through only one quadrant?
How about four quadrants? explain
What is the ratio 15 : 24 written in lowest terms?
a. 3 : 5
b. 5 : 8
c. 3 : 4
d. 7 : 8 user: ratio for 6 and 30?
its b i done the test
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(i.) (lim x->60-) f(x)
(ii.) (lim x->60+) f(x)
(iii.) What can you conclude about (lim x->60) f(x)? How is this shown by the graph?
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daniel team scored 40 points at the game danielscored 50% of the teams points how many poits did daniel scored
Which ordered pair is a solution to this equation?
(x+3)y = 14
A. (3, 2)
B. (5, 2)
C. (11, 1)
D.(7, 2)
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a. 12(20 + 2)
b. 22(10 + 2)
c. 10(2 · 22)
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