F(x) = 1/2x +4
replace f(x) with y
y = 1/2x+4
switch x and y
x = 1/2y +4
solve for y
multiply both sides by 2
2x = y+8
subtract 8 from both sides
2x-8 = y
rewrite with y on the left side: y = 2x-8
replace y with f(x)^-1 (inverse notation)
f(x)^-1 = 2x-8
solve for f^-1(4)
replace x with 4 in the equation and solve:
2(4) -8 = 8-8 = 0
Answer:
14.28 < h < 15
She can and would need to work 14.28 hours.
Step-by-step explanation:
To find how many hours she needs to work to earn $100, we need to know how much she is paid per hour. This amount is x because it is unknown. So 12 hours at x rate equals 84. This is 12x=84 so x=$7 per hour.
To earn a 100, she will earn $7 a hour but not work more than 15 hours. So we write the equation 100=7h where h is number of hours. Solve and h = 14.28. So Sylvia must work 14.28 < h < 15 to earn 100.
Answer:
the positive and negative square root of 196 is 14
Step1: Define an odd integer.
Define the first odd integer as (2n + 1), for n = 0,1,2, ...,
Note that n is an integer that takes values 0,1,2, and so no.
Step 2: Create four consecutive odd integers.
Multiplying n by 2 guarantees that 2n will be zero or an even number.
Therefore (2n + 1) is guaranteed to be an odd number.
By adding 2 to the odd integer (2n+1), the next number (2n+3) will also be an odd integer.
Let the four consecutive odd integers be
2n+1, 2n +3, 2n +5, 2n +7
Step 3: require that the four consecutive integers sum to 160.
Because the sum of the four consecutive odd integers is 160, therefore
2n+1 + 2n+3 + 2n+5 + 2n +7 = 160
8n + 16 = 160
8n = 144
n = 18
Because 2n = 36, the four consecutive odd integers are 37, 39, 41, 43.
Answer: 37,39,41,43