Write an exponential function to model the situation. A population of 470 animals decreases at an annual rate of 12%.
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Answer:
f inverse of x is equal to 3 to the power of the quantity x plus 6 end quantity minus 5 all over 4
Step-by-step explanation:
The function can be thought of as a series of steps, one operation at a time:
Start with x
Multiply by 4
Add 5
Take the
Subtract 6
That gives you a function value .
To get the inverse function, read that list from the bottom up (in reverse order, using inverse operations at each step).
Start with x (a bit confusing, because this x represents the function value you get at the end of the above list).
Add 6 (add is the inverse operation of subtract)
Raise 3 to the ...
Subtract 5
Divide by 4
Let's test this out. Find f(1).
Now put -4 into the inverse function.
The final result is the number we started with when we put 1 into <em>f</em>(<em>x</em>).
Finding an inverse is reversing the action of the function <em>f</em> by doing inverse operations in "backwards" order.
A lot of authors have you do this by switching x and y in the formula for a function, then solving for <em>x</em>.