How do you determine whether the function $f (x) = \sqrt{2 x + 3}$ $f(x)=sqrt(2x+3)$ 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 $= \frac{x^{2} - 3}{2}$ $=(x^2-3)/2$

The function is $f (x) = \sqrt{2 x + 3}$ $f(x)=sqrt(2x+3)$

The domain of $f (x)$ $f(x)$ is $x \in [- \frac{3}{2}, + \infty)$ $x in [-3/2,+oo)$

Let $y = \sqrt{2 x - 3}$ $y=sqrt(2x-3)$

Then,

$y^{2} = 2 x + 3$ $y^2=2x+3$

$2 x = y^{2} - 3$ $2x=y^2-3$

$x = \frac{y^{2} - 3}{2}$ $x=(y^2-3)/2$

When $x = \frac{3}{2}$ $x=3/2$ , $\Rightarrow$ $=>$ , $y = 0$ $y=0$

Changing $x$ $x$ and $y$ $y$

The inverse is

$y = \frac{x^{2} - 3}{2}$ $y=(x^2-3)/2$

And the domain of the inverse is $[0, + \infty)$ $[0,+oo)$

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