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]}

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