What is the inverse of f(x)=sqrt(e^{x^2)+3} ?

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

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inverse of f(x)=sqrt(e^{x^2)+3}

inverse

f (x) = e^{x^{2}} + 3

ln (x^{2} - 3), - ln (x^{2} - 3)

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = e^{y^{2}} + 3

ln (x^{2} - 3), - ln (x^{2} - 3)

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

f (x) = 5 ln (\frac{x + 2}{3})

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

f (x) = \frac{2 x}{3 x + 8}

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

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