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How do you find the inverse of #f(x)= 2x +3#?

Answer 1

Isaiah Anthony

#f^-1(x)=(x-3)/2#

#y=f(x)#

#y=2x+3#

Switch the places of #x# and #y:#

#x=2y+3#

Solve for #y:#

#2y=x-3#

#y=(x-3)/2#

#f^-1(x)=(x-3)/2#

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Answer 2

Abigail Allen

#y=(x-3)/2#

Now, the inverse of a function is just writing #x# in terms of #y#

So #f(x)=2x+3# becomes #y=2x+3#

#y=2x+3# becomes #y-3=2x#

#y-3=2x# becomes #(y-3)/2=x#

or #x=(y-3)/2#

Finally just interchange x and y because we want the function in terms of x. #y=(x-3)/2#

So #f^-1(x)=(x-3)/2#

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Answer 3

Jameson Allen

To find the inverse of ( f(x) = 2x + 3 ), follow these steps:

Replace ( f(x) ) with ( y ).
Swap ( x ) and ( y ): ( x = 2y + 3 ).
Solve for ( y ): ( y = \frac{x - 3}{2} ).
Replace ( y ) with ( f^{-1}(x) ): ( f^{-1}(x) = \frac{x - 3}{2} ).

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