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How do you find the inverse of #f(x)=x^2-6x#?

Answer 1

Chloe Alexander

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

First you equate #f(x)# to another variable, say #f(x)=y#.

But before that, complete the square for #f(x)#.

#:. x^2-6x+3^2-3^2=(x-3)^2-9#

Now, #y=(x-3)^2-9# #(x-3)^2=y+9# #(x-3)=sqrt(y+9)# #x=sqrt(y+9)+3#

Now swap back the x for the variable y.

So the inverse for #f(x)# is #f^-1(x)= sqrt(x+9)+3#

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Answer 2

Serenity Jones

To find the inverse of ( f(x) = x^2 - 6x ), follow these steps:

Replace ( f(x) ) with ( y ).
Swap ( x ) and ( y ) to get ( x = y^2 - 6y ).
Rearrange the equation to solve for ( y ): ( y^2 - 6y - x = 0 ).
Use the quadratic formula: ( y = \frac{{6 \pm \sqrt{{6^2 - 4(1)(-x)}}}}{{2(1)}} ).
Simplify the expression: ( y = \frac{{6 \pm \sqrt{{36 + 4x}}}}{{2}} ).
This gives you two possible values for ( y ), so the inverse functions are: ( f^{-1}(x) = 3 + \sqrt{{x + 9}} ) and ( f^{-1}(x) = 3 - \sqrt{{x + 9}} ).

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Answer from HIX Tutor

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