What is the inverse of f(x)= 1/3 (x^2+2)^{3/2} ?

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

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inverse of f(x)= 1/3 (x^2+2)^{3/2}

inverse

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

9^{\frac{1}{3}} x^{\frac{2}{3}} - 2, - 9^{\frac{1}{3}} x^{\frac{2}{3}} - 2

Solution steps

y = \frac{1}{3} (x^{2} + 2)^{\frac{3}{2}}

Replace

x

with

y

x = \frac{1}{3} (y^{2} + 2)^{\frac{3}{2}}

Solve for

y, x = \frac{1}{3} (y^{2} + 2)^{\frac{3}{2}}

9^{\frac{1}{3}} x^{\frac{2}{3}} - 2, - 9^{\frac{1}{3}} x^{\frac{2}{3}} - 2

\frac{1}{3} lo g_{10} (3 x)

f (x) = \frac{x - 2}{x ^{2} - 4}

f (x) = x^{4} - 32 x^{2} + 256

x^{2} ln (\frac{x}{6})

y + 4 = - \frac{5}{2} (x - 2)

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