What is the inverse of f(x)=9x^{-1/2}+16x^{1/2}-24 ?

The inverse of f(x)=9x^{-1/2}+16x^{1/2}-24 is

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inverse of f(x)=9x^{-1/2}+16x^{1/2}-24

inverse

f (x) = 9 x^{- \frac{1}{2}} + 16 x^{\frac{1}{2}} - 24

\frac{288 + 48 x + x ^{2} + x ^{\frac{3}{2}} ( x + 48 ) ^{\frac{1}{2}} + 24 ( x ( x + 48 ) ) ^{\frac{1}{2}}}{512}, \frac{288 + 48 x + x ^{2} - x ^{\frac{3}{2}} ( x + 48 ) ^{\frac{1}{2}} - 24 ( x ( x + 48 ) ) ^{\frac{1}{2}}}{512}

Solution steps

y = 9 x^{- \frac{1}{2}} + 16 x^{\frac{1}{2}} - 24

Replace

x

with

y

x = 9 y^{- \frac{1}{2}} + 16 y^{\frac{1}{2}} - 24

Solve for

y, x = 9 y^{- \frac{1}{2}} + 16 y^{\frac{1}{2}} - 24

\frac{288 + 48 x + x ^{2} + x ^{\frac{3}{2}} ( x + 48 ) ^{\frac{1}{2}} + 24 ( x ( x + 48 ) ) ^{\frac{1}{2}}}{512}, \frac{288 + 48 x + x ^{2} - x ^{\frac{3}{2}} ( x + 48 ) ^{\frac{1}{2}} - 24 ( x ( x + 48 ) ) ^{\frac{1}{2}}}{512}

f (x) = \frac{6 x}{5 x - 4}

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

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

\frac{3 x - 2}{4}

f (x) = f (x) (x)^{- 1} (7) = - 5 x + 2

What is the inverse of f(x)=9x^{-1/2}+16x^{1/2}-24 ?
The inverse of f(x)=9x^{-1/2}+16x^{1/2}-24 is