To find the inverse of this function, we first need to replace f(x) with y.
y = 2x^2 + 3
Now, we swap x and y
x = 2y^2 + 3
Now, we solve for y.
-3
x - 3 = 2y^2
Sqrt both sides.
√(x - 3) = 2y
Divide by 2
√(x - 3)/2 = y
Replace y with f^-1(x)
√(x - 3)/2 = f^-1(x)
Just realized you were asking for f(-1), not f^-1(x)
Feels bad.
f(-1) = 2(-1^2 + 3)
f(-1) = 2(-1^5)
f(-1) = 2(-1)
<u>f(-1) = -2</u>
I'm leaving the original answer in case you also need the inverse function. :)
Answer:
You will have to sell $7,667 worth of sales in a week in order for the straight commission offer to be at least as good
Step-by-step explanation:
Step 1: Get the total straight commission offer
We can express the straight total commission as follows;
A=R×T
where;
A=straight total commission
R=commission rate
T=total sales
In our case;
R=5%=5/100=0.05
T=t
replacing
A=0.05×t=0.05 t....equation 1
Step 2: Total amount of the second offer
We can express the total amount of the second offer as follows;
A=F+(R×T)
where;
A=amount of income the second company offers
F=fixed salary per week
R=commission rate
T=total sales
In our case;
F=$230 per week
R=2%=2/100=0.02
T=t
replacing;
A=230+(0.02×t)=0.02 t+230....equation 2
Step 3: Equate equation 1 and 2
0.05 t=0.02 t+230
(0.05 t-0.02 t)=230
0.03 t=230
t=230/0.03
t=7,666.67 rounded up=7,667
You will have to sell $7,667 worth of sales in a week in order for the straight commission offer to be at least as good
9 Polyester fill and 5 down fill sleeping bags were sold.
Step-by-step explanation:
Let,
Polyester fill sleeping bags = x
Down fill sleeping bags = y
Price of 1 polyester fill bag = $79
Price of 1 down fill bag = $149
According to given statement;
x+y=14 Eqn 1
79x+149y=1456 Eqn 2
Multiplying Eqn 1 by 79
![79(x+y=14)\\79x+79y=1106\ \ \ Eqn 3\\](https://tex.z-dn.net/?f=79%28x%2By%3D14%29%5C%5C79x%2B79y%3D1106%5C%20%5C%20%5C%20Eqn%203%5C%5C)
Subtracting Eqn 3 from Eqn 2
![(79x+149y)-(79x+79y)=1456-1106\\79x+149y-79x-79y=350\\70y=350](https://tex.z-dn.net/?f=%2879x%2B149y%29-%2879x%2B79y%29%3D1456-1106%5C%5C79x%2B149y-79x-79y%3D350%5C%5C70y%3D350)
Dividing both sides by 70
![\frac{70y}{70}=\frac{350}{70}\\y=5](https://tex.z-dn.net/?f=%5Cfrac%7B70y%7D%7B70%7D%3D%5Cfrac%7B350%7D%7B70%7D%5C%5Cy%3D5)
Putting y=5 in Eqn 1
![x+5=14\\x=14-5\\x=9\\](https://tex.z-dn.net/?f=x%2B5%3D14%5C%5Cx%3D14-5%5C%5Cx%3D9%5C%5C)
9 Polyester fill and 5 down fill sleeping bags were sold.
Keywords: Linear equations, subtraction
Learn more about linear equations at:
#LearnwithBrainly
Answer:
Lisa earned $247.50 for working 33 hours.
Step-by-step explanation:
WAY 1: proportional reasoning
7.50 x
------ = ----
1 h 33h
33 / 1 = 33
7.50 x 33 = 247.5
WAY 2: unit rate reasoning
7.50 per hour so x value of money for 33 h
7.50 x 33 = 247.5
The <em>correct answer</em> is:
It does not.
Explanation:
The scale of a graph just tells us how many units are between numbers. This does not change the overall distance represented.
For example, I can have two graphs on which the x-axis goes to 60. On one graph, I can count by 10s for my scale, while the other graph uses 5s. While the scales are different, the same distance is represented.