Write an addition equation that can help you find 9 - 6. Explain your answer
2 answers:
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9514 1404 393
Answer:
f⁻¹(x) = √((3 -x)/3)
Step-by-step explanation:
A function gives you a y-value for each value of x.
y = f(x)
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An inverse function tells you the x value that produced a given y-value. It is the solution to the equation ...
x = f(y)
So, we want to find y for ...
x = -3y² +3
x -3 = -3y² . . . . . . . . . . . subtract 3
(x -3)/-3 = y² . . . . . . . . . divide by -3
√((x -3)/-3) = y . . . . . . . take the square root.
The requirement for x > 0 in the original function means y > 0 for the inverse function. That is why we use the positive square root.
This can be simplified a little bit to remove the minus sign from the denominator.
f⁻¹(x) = √((3 -x)/3)
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The graph plots the function and its inverse. They are reflections of each other over the line y=x. (That's one way you can tell you have the correct inverse function.)
Answer:
a) 41
b) -31
c) 25/3
Step-by-step explanation:
The instructions explain what a function is pretty clearly.
Basically, whatever is in the parentheses next to the , you plug in to the expression that is the function.
ex:
Okay, onto the problems:
a)
First, plug in 14, since that is given:
and solve.
So, 41 is the answer to a.
b) Do the same thing you did in problem a. Plug in the number inside the parentheses and solve.
-31 is the answer to b.
c) For this problem, you have to do a bit of algebra.
First, take the base function f(x):
Then, set f(x) = 24:
and solve by isolating x.
25/3 is the answer to c.