How do you determine whether the function #f(x)=sqrt(2x+3)# has an inverse and if it does, how do you find the inverse function?

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Answer 1 · 2017-12-06T08:58:26

The inverse is #=(x^2-3)/2#

The function is #f(x)=sqrt(2x+3)#

The domain of #f(x)# is #x in [-3/2,+oo)#

Let #y=sqrt(2x-3)#

Then,

#y^2=2x+3#

#2x=y^2-3#

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

When #x=3/2#, #=>#, #y=0#

Changing #x# and #y#

The inverse is

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

And the domain of the inverse is #[0,+oo)#

graph{(y-sqrt(2x+3))(y-(x^2-3)/2)(y-x)=0 [-3, 10, -5, 5]}