Question 1190029: Assume f is a one-to-one function. If f(x)=3-6xf , find f^-1(33)
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
Assume f is a one-to-one function. If f(x)=3-6xf , find f^-1(33)
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The problem is presented very unprofessionally in this post.
If f(x) = 3 - 6x, then f(x) is a linear function of x. Since a coefficient at x is not equal to zero,
this function is one-to-one without any assumption: you don't need make this assumption - it is TRUE without any assumption.
So, the correct formulation should be in this form:
If f(x)=3-6x, find f^-1(33).
In Math, when you formulate a problem, all the words / (the terms) should be used correctly and must be placed in a right order.
Also, unnecessary words should not obscure a meaning of the problem and should not interfere with understanding.
It is the same as in music (classic music, I mean . . . )
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OK, now I will solve the problem. So, the question is
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| If f(x)=3-6x, find f^-1(33). |
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To get the answer, you do not need express f^(-1) (x) explicitly as a function of x.
In this problem, the KEY POINT is to understand that the question is equivalent to finding x from equation
f(x) = 33, which is 3 - 6x = 33.
From this equation, you have
3 - 33 = 6x
-30 = 6x
x = (-30)/6 = -5.
ANSWER. f^(-1)(33) = -5.
CHECK. f(-5) = 3 - 6(-5) = 3 + 30 = 33. ! Precisely correct !
Solved, answered and explained, including all incoming details.
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The lesson to learn from my post
(1) To get the answer, you do not need express f^(-1) (x) explicitly as a function of x.
(2) In this problem, the question is equivalent to finding x from equation for a base function.
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