Question 1190029
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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:


<pre>
        If f(x)=3-6x, find f^-1(33).
</pre>

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


<pre>
    +----------------------------------+
    |    If f(x)=3-6x, find f^-1(33).  |
    +----------------------------------+


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.


<U>ANSWER</U>.  f^(-1)(33) = -5.


<U>CHECK</U>.   f(-5) = 3 - 6(-5) = 3 + 30 = 33.   ! Precisely correct !
</pre>

Solved, answered and explained, including all incoming details.



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<H3>The lesson to learn from my post</H3>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1) &nbsp;&nbsp;To get the answer, &nbsp;you do not need express &nbsp;f^(-1) (x) &nbsp;explicitly as a function of &nbsp;x.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2) &nbsp;&nbsp;In this problem, the question is equivalent to finding x from equation for a base function.