Let's complete the square
f(x) = x^2 + 6x + 8
y = x^2 + 6x + 8
y-8 = x^2 + 6x
y-8+9 = x^2+6x+9 .... see note below
y+1 = (x+3)^2
y = (x+3)^2-1
note: I added 9 to both sides due to taking half of the 6, and then squaring that result.
We'll restrict x such that 
to ensure that this function is one-to-one.
Now we need to swap x and y, and solve for y to get the inverse
y = (x+3)^2 - 1
x = (y+3)^2 - 1
x+1 = (y+3)^2
(y+3)^2 = x+1
y+3 = sqrt(x+1)
y = sqrt(x+1)-3
g(x) = sqrt(x+1)-3 is the inverse
The graph is shown below. The original function is in red. The inverse is in blue. The inverse is the result of reflecting the red curve over the dashed line y = x. So this explains why x and y swap places. Consequently, the domain and range also swap as well.
Answer:
4
Step-by-step explanation:
f(x) = 4 ^ ( x-2)
Let x=3
f(3) = 4 ^ ( 3-2)
= 4 ^ 1
= 4
9,736 rounded to the nearest ten is 9,740
Answer:
3.14 thousand dollars
Step-by-step explanation:
Standard deviation is the average distance of your data values from the mean (basically, how far off you were from the center). We calculate standard deviation or σ by taking each value, subtracting it from the mean, squaring it, then dividing by the mean.
First, we need to find the mean, which is the sum of all values / number of values.
5 + 6 + 5 + 10 + 9 = 35 / 5 = 7
Take the absolute value of the difference of each value from 7:
5 - 7 = 2
6 - 7 = 1
5 - 7 = 2
10 - 7 = 3
9 - 7 = 2
Square each of these values and add them together:
2^2 + 1^2 + 2^2 + 3^2 + 2^2 = 22
Divide the sum by the mean:
22 / 7 = 3.14
<u>The standard deviation is 3.14 thousand dollars.</u>
