Answer:
The answers is: f(x) domain: x ≥ 0
f–1(x) range: y ≥ 0
Step-by-step explanation:
By restricting the domain of f(x) by x ≥ 0 you can now have an inverse function for f(x) = x2 + 3. Also the domain of f(x) is equal to the range of f–1(x).
Answer:
The integral diverges
Step-by-step explanation:
Consider the integral from 0 to infinity of
![xe^{4x}](https://tex.z-dn.net/?f=xe%5E%7B4x%7D)
We can do this in parts
![\int {xe^{4x} } \, dx =\int {x} \, d(e^{4x})/4\\ = x/4 e^{4x}-e^{4x}/16](https://tex.z-dn.net/?f=%5Cint%20%7Bxe%5E%7B4x%7D%20%7D%20%5C%2C%20dx%20%3D%5Cint%20%7Bx%7D%20%5C%2C%20d%28e%5E%7B4x%7D%29%2F4%5C%5C%20%3D%20x%2F4%20e%5E%7B4x%7D-e%5E%7B4x%7D%2F16)
When we substitute limits infinity we find that the values become infinity
Hence the integral diverges
The given improper integral diverges
Answer:
40 gallons of water and 140 gallons premium antifreeze
Step-by-step explanation:
Let p represent the number of gallons of premium antifreeze in the mix. Then 180-p is the number gallons of water. The amount of pure antifreeze in the mix is then ...
0.90p + 0·(180 -p) = 0.70·180
p = 0.70·180/0.90 = 140 . . . . divide by the coefficient of p
180-p = 40 . . . . . find the water content
40 gallons of water and 140 gallons of premium antifreeze are in the mix.
The answer to this equation is -53. This is because 7 times -5 equals -35. -35-2 equals -37. -3 times 8 equals -24. -24 plus 8 equals -16. -37+(-16)= -53
Answer:
$196
Step-by-step explanation:
Step one
given data
We are told that Noel bought a printer for $10 less than half its original price
let the original price be x
hence Noel paid = x/2-10= 88
Step two
amount paid= x/2-10= 88
Collect like terms
x/2= 88+10
x/2= 98
cross multiply
x=196
Hence the original price is $196