if F(x)=(Sqrt(2x+1)-2) find the inverse function F(^-1)(X)

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rwolff912 | (Level 1) Adjunct Educator

Posted on

I remeber that when I am looking for an inverse I am looking for a function that does the opposite of this function. So first I switch the x and y. 



Then I solve for y by undoing operations to get the y by itself. 


`+2 +2 `

`x+2=sqrt(2y+1) `



`-1 = -1`






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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

We have to solve an equation y=sqrt(2x+1)-2 for x. It is easy:

y+2 = sqrt(2x+1),

(y+2)^2 = (2x+1),

x = (1/2)*[(y+2)^2 - 1].

We must also note that the original y(x) has values from -2 to +infinity, therefore x(y) is defined for y>=-2 only.

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balajia | College Teacher | (Level 1) eNoter

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Let F(x)=y