Answer:
f(x) = 8(x-3)
Step-by-step explanation:
F^ -1 ( x) = x/8 +3
Let y = x/8+3
To find the inverse
Exchange x and y
x = y/8+3
Solve for y
x-3 = y/8+3-3
x-3 = y/8
Multiply each side by 8
8(x-3) = y/8 * 8
8(x-3) = y
The inverse of the inverse is the function so
f(x) = 8(x-3)
Answer:
3, in both a), b)
Step-by-step explanation:
a) The slope of the line tangent to the curve that passes through the point (2,-10) is equal to the derivative of p at x=2.
Using differentiation rules (power rule and sum rule), the derivative of p(x) for any x is 
. In particular, the value we are looking for is 
.
If you would like to compute the equation of the tangent line, we can use the point-slope equation to get 
b) The instantaneus rate of change is also equal to the derivative of P at the point x=2, that is, P'(2). This is equal to 
.
Answer:
O It has the same slope and a different y-intercept.
Step-by-step explanation:
y = mx + b
m = 3/8
b = 12
y = (3/8)x + 12
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Data in the table: slope is the rise (y) over the run (x) between two points (assuming the data represent a linear line).
Change in x and y between two points. I'll choose (-2/3,-3/4) and (1/3,-3/8).
Change in y: (-3/8 - (-3/4)) = (-3/8 - (-6/8)) = 3/8
Change in x: (1/3 - (-2/3)) = (1/3+2/3) = 3/3 = 1
Slope = (Change in y)/(Change in x) = (3/8)/1 = 3/8
The slope of the equation is the same as the data in the table.
Now let's determine if the y-intercept is also the same (12). The equation for the data table is y = (2/3)x + b, and we want to find b. Enter any of the data points for x and y and then solve for b. I'll use (-2/3, -3/4)
y = (3/8)x + b
Use (-2/3, -3/4)
-3/4 =- (3/8)(-2/3) + b
-3/4 = (-6/24) + b
b = -(3/4) + (6/24)
b = -(9/12) + (3/12)
b = -(6/12)
b = -(1/2)
The equation of the line formed by the data table is y = (3/8)x -(1/2)
Therefore, It has the same slope and a different y-intercept.
Answer:
Step-by-step explanation:
