Question #61176

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Answer 1 · 2014-11-16T11:34:34

Step 1: Replace #f(x)# by #y#.

#y=6x-x^2#

Step 2: Solve for #x#.

By rearranging terms,

#=>x^2-6x=y#

by adding #9#,

#=>x^2-6x+9=y+9#

by completing the square,

#=>(x-3)^2=y+9#

by taking the square-root,

#=>x-3=pm sqrt{y+9}#

by adding #3#,

#=> x=3 pm sqrt{y+9}#

since #x>3#,

#=> x=3+sqrt{y+9}#

Step 3: Exchange #x# and #y#.

#=> y=3+sqrt{x+9}#

Step 4: Replace #y# by #f^{-1}(x)#.

#=> f^{-1}(x)=3+sqrt{x+9}#

I hope that this was helpful.