Select the correct answer.
1 answer:
9514 1404 393
Answer:
A. f^-1(x) = x³ -12
Step-by-step explanation:
The inverse function can be found by solving ...
x = f(y)
x = ∛(y +12) . . . . . use the definition of f(x)
x³ = y +12 . . . . . . . cube both sides to eliminate the radical
x³ -12 = y . . . . . . . add -12 to isolate the y-variable
f^-1(x) = x³ -12 . . . matches choice A
You might be interested in
Answer: Anything between 0 and 10, excluding both endpoints.
In terms of symbols we can say 0 < w < 10 where w is the width.
===================================================
Explanation:
You could do this with two variables, but I think it's easier to instead use one variable only. This is because the length is dependent on what you pick for the width.
w = width
2w = twice the width
2w-5 = five less than twice the width = length
So,
- width = w
- length = 2w-5
which lead to
area = length*width
area = (2w-5)*w
area = 2w^2-5w
area < 150
2w^2 - 5w < 150
2w^2 - 5w - 150 < 0
To solve this inequality, we will solve the equation 2w^2-5w-150 = 0
Use the quadratic formula. Plug in a = 2, b = -5, c = -150
Ignore the negative solution as it makes no sense to have a negative width.
The only practical root is w = 10.
If w = 10 feet, then the area = 2w^2-5w results in 150 square feet.
----------------------
Based on that root, we need to try a sample value that is to the left of it.
Let's say we try w = 5.
2w^2 - 5w < 150
2*5^2 - 5*5 < 150
25 < 150 ... which is true
This shows that if 0 < w < 10, then 2w^2-5w < 150 is true.
Now try something to the right of 10. I'll pick w = 15
2w^2 - 5w < 150
2*15^2 - 5*15 < 150
375 < 150 ... which is false
It means w > 10 leads to 2w^2-5w < 150 being false.
Therefore w > 10 isn't allowed if we want 2w^2-5w < 150 to be true.
Answer:
Step-by-step explanation:
The given system is
3x-2y=6
0.4(20y+15)=x
The slope intercept form is y=mx+c.
For the first equation, 3x-2y=6, we add -3x to both side -2y=-3x+6
For 0.4(20y+15)=x, we expand to get:
Divide through by 8
Therefore the system in slope-intercept form is: