Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.
The radius of a circle is
always half of the diameter of the circle. In this case, the diameter is
, meaning that when we halve
, we will get our radius. Therefore, the radius of the circle is
. Hope this has helped you understand and have a great day!
Answer:
see explanation
Step-by-step explanation:
(
)(t) = 
= 
Answer:
-5 ≤ y ≤ 5
Step-by-step explanation:
maximum y value is 5
minimum y value is -5
-5 ≤ y ≤ 5
We can create two points.
30 feet below the surface of the water 10 seconds after he entered the water
100 feet below the surface after 40 seconds
So we have (10, 30) and (40, 100)
Plug this values into the slope formula:
m = y2-y1/x2-x1
m = (100 - 30)/(40 - 10)
m = 70/30
m = 2 1/3
