Which functions are the same as their inverse functions
1 answer:
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Answer:
The domain is
The range is
Step-by-step explanation:
we have
<em>Find the domain</em>
Remember that
The domain of a function is the set of all possible values of x
we know that the radicand of the function must be greater than or equal to zero
so
solve for x
therefore
The domain is
<em>Find the range</em>
Remember that
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
For x=7
The value of y is equal to
so
The solution for y is the interval [1,∞)
therefore
The range is
Answer:
(1,6)
x = 1, y = 6
See attachment for the graph
Step-by-step explanation:
y=x+5
y=-x+7
Using the elimination process
y=x+5
- y=-x+7
----------------
0=2x-2
2=2x
1=x
x=1
Substitute x = 1
y = x + 5
y = 1 + 5
y = 6
Answer:
Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.
Step-by-step explanation:
Let tap B fills the pool alone in the time = x hours
So in one hour part of pool will be filled =
Another tap A when turned on, it takes time to fill the pool = x-5 hours
So in one hour part of the same pool filled =
Now both the taps A and B are turned on then time taken to fill the pool = 3 hours.
Part of the pool filled in one hour by both the taps =
Now we form an equation
Part of pool filled in one hour by tap A + Part of pool filled in one hour by tap B = Part of pool filled in one hour by both the taps when turned on
3(x - 4) = x(x - 5)
x² -5x = 3x - 12
x² - 8x + 12 = 0
x² - 6x - 2x + 12 = 0
x(x - 6) - 2(x - 6) = 0
(x -2)(x - 6) = 0
x = 2, 6 hours
We will take higher value of x as x = 6 hours for tap B.
Time taken by tap A = 6 - 4 = 2 hours.
Therefore, Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.