How do you find the inverse of #f(x)= -sqrt(2x+1)#?

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Answer 1 · 2018-03-31T13:55:14

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

To find the inverse we need to express #x# as a function of #y#:

#y=-sqrt(2x+1)#

Square both sides:

#y^2=2x+1#

#y^2-1=2x#

#x=(y^2-1)/2#

#x=1/2y^2-1/2#

Substitute:

#y=x#

#y=1/2x^2-1/2#

#:.#

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

Notice that the negative half of the graph of #1/2x^2-1/2# is the graph of

#-sqrt(2x+1)# reflected in the line #y=x#. This is typical for the inverse of a function.

GRAPH:

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