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

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

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

inverse

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

\frac{ln ^{2} ( x )}{ln ^{2} ( 3 )} + 3

Solution steps

y = 3^{x - 3}

Replace

x

with

y

x = 3^{y - 3}

Solve for

y, x = 3^{y - 3}

\frac{ln ^{2} ( x )}{ln ^{2} ( 3 )} + 3

x^{4} + 3

f (x) = 5 + x + 4 2 x + 1

f (x) = 2 - e^{(- \frac{1}{3} y)}

f (x) = x + 5 - 8

y = \frac{3 x - 4}{2 - x}

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