What is the inverse of f(x)=(8x^{1/2}-3)^7 ?

The inverse of f(x)=(8x^{1/2}-3)^7 is (x^{2/7})/(64)+(3\sqrt[7]{x})/(32)+9/64

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inverse of f(x)=(8x^{1/2}-3)^7

inverse

f (x) = (8 x^{\frac{1}{2}} - 3)^{7}

\frac{x ^{\frac{2}{7}}}{64} + \frac{3 7 x}{32} + \frac{9}{64}

Solution steps

y = (8 x^{\frac{1}{2}} - 3)^{7}

Replace

x

with

y

x = (8 y^{\frac{1}{2}} - 3)^{7}

Solve for

y, x = (8 y^{\frac{1}{2}} - 3)^{7}

\frac{x ^{\frac{2}{7}}}{64} + \frac{3 7 x}{32} + \frac{9}{64}

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

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

lo g_{10} (x - 9) + 1

f (x) = \frac{( 2 x + 3 )}{5 x + 4}

\frac{3 x - 4}{x - 1}

What is the inverse of f(x)=(8x^{1/2}-3)^7 ?
The inverse of f(x)=(8x^{1/2}-3)^7 is (x^{2/7})/(64)+(3\sqrt[7]{x})/(32)+9/64