Answer:
3. Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.
Step-by-step explanation:
The domain of a function is the range of its inverse, and vice versa. The only answer choice that expresses this relationship is choice 3.
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Comment on the answer choice:
The slope of the function is undefined at x=4, so restricting the function domain to the portion with positive slope means the domain restriction of the function is x > 4. That also means the range restriction of the function is y > 6. The domain restriction of the inverse function is the same: x > 6, not x ≥ 6. The answer choice has an error.
<span>Triangle Inequality Theorem
</span><span>the sum of two side lengths of a triangle is always greater than the third side.
</span>
5+8=13
your answer = no
Answer:
Not exactly sure what "funny numbers" are but I'm assuming you mean prime numbers? In that case there are a total of 7 prime numbers between 30 and 60.
Step-by-step explanation:
Answer:
(5,-6)
Step-by-step explanation:
ONE WAY:
If 
, then 
.
Let's simplify that.
Distribute with 
:
Combine the end like terms 
:
Use 
identity for 
:
Combine like terms 
and 
:
We are given 
.
So we have that 
.
The vertex happens at 
.
Compare 
to 
to determine 
.
Let's plug it in.
So the 
coordinate is 5.
Let's find the corresponding 
coordinate by evaluating our expression named 
at 
:
So the ordered pair of the vertex is (5,-6).
ANOTHER WAY:
The vertex form of a quadratic is 
where the vertex is 
.
Let's put 
into this form.
We are given .
We will need to complete the square.
I like to use the identity 
.
So If you add something in, you will have to take it out (and vice versa).
So we have in vertex form is:
.
The vertex is (3,-6).
So if we are dealing with the function .
This means we are going to move the vertex of right 2 units to figure out the vertex of which puts us at (3+2,-6)=(5,-6).
The coordinate was not effected here because we were only moving horizontally not up/down.
