document.write( "Question 1117120: Given that f(x) = 6x – 3, find the following:\r
\n" ); document.write( "\n" ); document.write( "(f^-1)(x) =
\n" ); document.write( "f(2) =
\n" ); document.write( "(f^-1)(-5) =\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "

Algebra.Com's Answer #732127 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Notice that another way to find the inverse of a simple function like this is to use the fact that an inverse function \"un-does\" what the function does.

\n" ); document.write( "The given function takes the input value, multiplies it by 6, and subtracts 3. To undo that, the inverse function needs to do the opposite operations in the opposite order: add 3 and divide by 6 --> $\"%28x%2B3%29%2F6\"$ which is of course the same as the answer from the other tutor, $\"x%2F6%2B1%2F2\"$ .

\n" ); document.write( "Also notice that you don't need to find the inverse function to evaluate (f^-1)(-5).

\n" ); document.write( "When you are asked to evaluate (f^-1)(-5), the definition of an inverse function tells you that you are to find the value of the input value for which the given function value is -5:

\n" ); document.write( " $\"6x-3+=+-5\"$
\n" ); document.write( " $\"6x+=+-2\"$
\n" ); document.write( " $\"x+=+-1%2F3\"$

\n" ); document.write( "This is the same answer you get if you evaluate the inverse function at -5:

\n" ); document.write( " $\"%28-5%2B3%29%2F6+=+-2%2F6+=+-1%2F3\"$ \n" ); document.write( "

\n" );