If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
2 answers:
Answer:
Step-by-step explanation:
If f(x) and it's inverse function plot on same coordinate plane.
Both graph intersect at line y=x because y=x is line of symmetry of inverse function.
Intersection of and f(x) would be x and y coordinate same.
Therefore,
We are given four options. Let we check each one.
Option 1: (0,-2)
x=0 and y=-2 , 0≠-2
This is false.
Option 2: (1,-1)
x=1 and y=-1 , 1≠-1
This is false.
Option 3: (2,0)
x=2 and y=0 , 2≠0
This is false.
Option 4: (3,3)
x=3 and y=3 , 3=3
This is true.
Thus, (3,3) is point of intersection of
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Answer:
Carbon-14 loses around 10% ( 0.1 in decimal form) of its mass, after one millennium.
Then if we start with a mass A of Carbon-14, after one millennium we will have a mass equal to:
A - A*0.1 = A*(0.9)
After another millennium, we will have a mass equal to:
A*(0.9) - A*(0.9)*0.1 = A*(0.9)^2
And so on, this is an exponential decay.
We already can see the pattern here, after x millenniums, the mass of carbon-14 will be:
M(x) = A*(0.9)^x
Now, in this problem we have 600 grams of carbon-14, then the equation for the mass will be:
y = M(x) = 600g*(0.9)^x
And the graph of this equation is shown below.
