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

The inverse of f(x)=sqrt(3x^e)-2 is ((x^2+4x+4)/3)^{9545/25946}

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

inverse

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

(\frac{x ^{2} + 4 x + 4}{3})^{\frac{9545}{25946}}

Solution steps

y = 3 x^{e} - 2

Replace

x

with

y

x = 3 y^{e} - 2

Solve for

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

(\frac{x ^{2} + 4 x + 4}{3})^{\frac{9545}{25946}}

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

(3 x^{2} - 31 x + 56) - (x - 8)

f (x) = (x - 2)^{2} + (y - 6)^{2} = 25

f (x) = 3^{x} + 8

f (x) = 2 x - 10

What is the inverse of f(x)=sqrt(3x^e)-2 ?
The inverse of f(x)=sqrt(3x^e)-2 is ((x^2+4x+4)/3)^{9545/25946}