What is the inverse of f(x)=2sqrt(x+3)-1 ?

The inverse of f(x)=2sqrt(x+3)-1 is (x^2+1)/4+x/2-3

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inverse of f(x)=2sqrt(x+3)-1

inverse

f (x) = 2 x + 3 - 1

\frac{x ^{2} + 1}{4} + \frac{x}{2} - 3

Solution steps

y = 2 x + 3 - 1

Replace

x

with

y

x = 2 y + 3 - 1

Solve for

y, x = 2 y + 3 - 1

\frac{x ^{2} + 1}{4} + \frac{x}{2} - 3

y = 6 x + 7

\frac{3 x + 2}{2 x - 5}

f (x) = \frac{4 x - 3}{2 x + 1}

f (x) = 4 - x + 2

- 2 x^{3} + 1

What is the inverse of f(x)=2sqrt(x+3)-1 ?
The inverse of f(x)=2sqrt(x+3)-1 is (x^2+1)/4+x/2-3