What is the inverse of 3/4 x^{4/3}-3/8 x^{2/3}+9 ?

The inverse of 3/4 x^{4/3}-3/8 x^{2/3}+9 is

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inverse of 3/4 x^{4/3}-3/8 x^{2/3}+9

inverse

\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}} + 9

\frac{( 3 + ( 192 x - 1719 ) ^{\frac{1}{2}} ) ^{\frac{3}{2}}}{24 \cdot 3 ^{\frac{1}{2}}}, - \frac{( 3 + ( 192 x - 1719 ) ^{\frac{1}{2}} ) ^{\frac{3}{2}}}{24 \cdot 3 ^{\frac{1}{2}}}, \frac{( 3 - ( 192 x - 1719 ) ^{\frac{1}{2}} ) ^{\frac{3}{2}}}{24 \cdot 3 ^{\frac{1}{2}}}, - \frac{( 3 - ( 192 x - 1719 ) ^{\frac{1}{2}} ) ^{\frac{3}{2}}}{24 \cdot 3 ^{\frac{1}{2}}}

Solution steps

y = \frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}} + 9

Replace

x

with

y

x = \frac{3}{4} y^{\frac{4}{3}} - \frac{3}{8} y^{\frac{2}{3}} + 9

Solve for

y, x = \frac{3}{4} y^{\frac{4}{3}} - \frac{3}{8} y^{\frac{2}{3}} + 9

\frac{( 3 + ( 192 x - 1719 ) ^{\frac{1}{2}} ) ^{\frac{3}{2}}}{24 \cdot 3 ^{\frac{1}{2}}}, - \frac{( 3 + ( 192 x - 1719 ) ^{\frac{1}{2}} ) ^{\frac{3}{2}}}{24 \cdot 3 ^{\frac{1}{2}}}, \frac{( 3 - ( 192 x - 1719 ) ^{\frac{1}{2}} ) ^{\frac{3}{2}}}{24 \cdot 3 ^{\frac{1}{2}}}, - \frac{( 3 - ( 192 x - 1719 ) ^{\frac{1}{2}} ) ^{\frac{3}{2}}}{24 \cdot 3 ^{\frac{1}{2}}}

f (x) = \frac{- 5 x + 1}{5 x - 2}

f (x) = lo g_{7} (x - 1)

2 + \frac{1}{x ^{2} - 3 x}

12 x

f (x) = 9 x^{2} + 1

What is the inverse of 3/4 x^{4/3}-3/8 x^{2/3}+9 ?
The inverse of 3/4 x^{4/3}-3/8 x^{2/3}+9 is