Han wants to buy a $30 ticket to a game, but the pre-order tickets are sold out. He knows there will be more tickets sold the da
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Answer:
g and f are inverse functions because g(f(x)) = f(g(x)) = x
Step-by-step explanation:
Let's start by finding f(g(x)) and g(f(x)). As we discussed in another question, to find a composite function, apply the outer function to whatever the inner function evaluates to. We can start with f(g(x)):
Now, let's find g(f(x)):
There is a property that says that if f(g(x)) = g(f(x)) = x, the two functions are inverse. This suggests that g and f are inverse functions. We can verify this by taking one function, switching y and x, and then solving for y. If we complete this process and find that we get the OTHER function, it means the two functions are inverse. Let's try that:
Swap x and y:
Solve for y:
Notice that we got g, which means f and g are inverse.
Salt flows into the tank at a rate of
(1/2 lb/gal) * (6 gal/min) = 3 lb/min
and flows out at a rate of
(Q(t)/60 lb/gal) * (6 gal/min) = 6Q(t) lb/min
The net rate of change of the amount of salt in the tank at time is then governed by
Solve for :
The tank starts with 10 lb of salt, so that Q(0) = 10. This gives us
so that the amount of salt in the tank at time is given by
Answer:
Step-by-step explanation:
Per cent means ' out of a hundred' , thus
45% = ← divide ( cancel) both 45 and 100 by 5
45% = ← in simplest form