In order for a function to have an inverse that is also a function there are 2 main requirements:
1. The function should be bijective (ie) the function should be one-one ( each element in codomain has not more than 1 pre image in domain) and onto ( Range should be equal to codomain)
2. The inverse function should be defined by a suitable domain and range
Hope this answer helps you..
To find the maximum or minimum value of a function, we can find the derivative of the function, set it equal to 0, and solve for the critical points.
H'(t) = -32t + 64
Now find the critical numbers:
-32t + 64 = 0
-32t = -64
t = 2 seconds
Since H(t) has a negative leading coefficient, we know that it opens downward. This means that the critical point is a maximum value rather than a minimum. If we weren't sure, we could check by plugging in a value for t slightly less and slighter greater than t=2 into H'(t):
H'(1) = 32
H'(3) = -32
As you can see, the rate of change of the object's height goes from increasing to decreasing, meaning the critical point at t=2 is a maximum.
To find the height, plug t=2 into H(t):
H(2) = -16(2)^2 +64(2) + 30 = 94
The answer is 94 ft at 2 sec.
Answer:
x + 2, x ≠ -2
Step-by-step explanation:
Note that F(x) = x^2 + 4x + 4 factors into (x + 2)^2, and that we are dividing this by g(x) = x + 2. The quotient is x + 2, which in this problem has been named h(x).
The quotient (f/g)(x) is therefore x + 2 EXCEPT that this is not defined at x = -2, because the denominator, x + 2, will be zero there, undefined.
<span>x cubed +3x squared - 4x= 0
= x^3 + 3x^2 -4x = 0
=x(x^2 +3x -4) = 0
= x (x+4)(x-1) = 0
x = 0
x+ 4 = 0 then x = -4
x - 1 = 0 then x = 1
answer: x = 0, x = -4 and x = 1</span>
Find the vertex:
Determine if the parabola will open up or down:
Since the value of a is positive, the parabola will open upwards
Find the x and y intercepts:
Factor 
to find the x intercepts
(x+8)(x+2)
x + 8 = 0
x = -8
x + 2 = 0
x = -2
x intercepts:
x = -2
x = -8
Find the y intercept
Hence, C. Graph A best represents the quadratic function
