What is the inverse of f(x)=(x/4-5)^{1/3}+3/7 ?

The inverse of f(x)=(x/4-5)^{1/3}+3/7 is 4x^3+6752/343-(36x^2)/7+(108x)/(49)

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inverse of f(x)=(x/4-5)^{1/3}+3/7

inverse

f (x) = (\frac{x}{4} - 5)^{\frac{1}{3}} + \frac{3}{7}

4 x^{3} + \frac{6752}{343} - \frac{36 x ^{2}}{7} + \frac{108 x}{49}

Solution steps

y = (\frac{x}{4} - 5)^{\frac{1}{3}} + \frac{3}{7}

Replace

x

with

y

x = (\frac{y}{4} - 5)^{\frac{1}{3}} + \frac{3}{7}

Solve for

y, x = (\frac{y}{4} - 5)^{\frac{1}{3}} + \frac{3}{7}

4 x^{3} + \frac{6752}{343} - \frac{36 x ^{2}}{7} + \frac{108 x}{49}

What is the inverse of f(x)=(x/4-5)^{1/3}+3/7 ?
The inverse of f(x)=(x/4-5)^{1/3}+3/7 is 4x^3+6752/343-(36x^2)/7+(108x)/(49)