What is the inverse of f(x)=6x^{1/4}+5 ?

The inverse of f(x)=6x^{1/4}+5 is (x^4)/(1296)-(5x^3)/(324)+(25x^2)/(216)-(125x)/(324)+625/1296

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inverse of f(x)=6x^{1/4}+5

inverse

f (x) = 6 x^{\frac{1}{4}} + 5

\frac{x ^{4}}{1296} - \frac{5 x ^{3}}{324} + \frac{25 x ^{2}}{216} - \frac{125 x}{324} + \frac{625}{1296}

Solution steps

y = 6 x^{\frac{1}{4}} + 5

Replace

x

with

y

x = 6 y^{\frac{1}{4}} + 5

Solve for

y, x = 6 y^{\frac{1}{4}} + 5

\frac{x ^{4}}{1296} - \frac{5 x ^{3}}{324} + \frac{25 x ^{2}}{216} - \frac{125 x}{324} + \frac{625}{1296}

What is the inverse of f(x)=6x^{1/4}+5 ?
The inverse of f(x)=6x^{1/4}+5 is (x^4)/(1296)-(5x^3)/(324)+(25x^2)/(216)-(125x)/(324)+625/1296