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

The inverse of f(x)=3-sqrt(ln(x^2+2x-3)) is -1+sqrt(e^{x^2-6x+9)+4},-sqrt(e^{x^2-6x+9)+4}-1

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

inverse

f (x) = 3 - ln (x^{2} + 2 x - 3)

- 1 + e^{x^{2} - 6 x + 9} + 4, - e^{x^{2} - 6 x + 9} + 4 - 1

Solution steps

y = 3 - ln (x^{2} + 2 x - 3)

Replace

x

with

y

x = 3 - ln (y^{2} + 2 y - 3)

Solve for

y, x = 3 - ln (y^{2} + 2 y - 3)

- 1 + e^{x^{2} - 6 x + 9} + 4, - e^{x^{2} - 6 x + 9} + 4 - 1

f (x) = x + (\frac{4}{x})

f (x) = \frac{10 x - 6}{2 x - 2}

f (x) = - \frac{3 x - 7}{x}

f (x) = \frac{5 x - 9}{x - 2}

f (x) = - 2 (x + 1)^{2} + 3

What is the inverse of f(x)=3-sqrt(ln(x^2+2x-3)) ?
The inverse of f(x)=3-sqrt(ln(x^2+2x-3)) is -1+sqrt(e^{x^2-6x+9)+4},-sqrt(e^{x^2-6x+9)+4}-1