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

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

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

inverse

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

ln (x) + 3, - ln (x) + 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) + 3, - ln (x) + 3

ln (3 x - 5) - ln (x + 9) + 5

f (x) = x^{2} + x - 6

f (x) = \frac{5 x - 1}{3}

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

y = \frac{x + 1}{x}

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