What is the inverse of f(x)=(x^2)/(200)+x/6 ?

The inverse of f(x)=(x^2)/(200)+x/6 is (10(sqrt(18x+25)-5))/3 ,-(10(sqrt(18x+25)+5))/3

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inverse of f(x)=(x^2)/(200)+x/6

inverse

f (x) = \frac{x ^{2}}{200} + \frac{x}{6}

\frac{10 ( 18 x + 25 - 5 )}{3}, - \frac{10 ( 18 x + 25 + 5 )}{3}

Solution steps

y = \frac{x ^{2}}{200} + \frac{x}{6}

Replace

x

with

y

x = \frac{y ^{2}}{200} + \frac{y}{6}

Solve for

y, x = \frac{y ^{2}}{200} + \frac{y}{6}

\frac{10 ( 18 x + 25 - 5 )}{3}, - \frac{10 ( 18 x + 25 + 5 )}{3}

- \frac{ln ( 5 y - 6 )}{20}

f (x) = - \frac{4}{3} x - \frac{1}{2}

y = 4^{\frac{x}{2}}

f (x) = (\frac{6 e ^{x} - 4}{8 e ^{x} + 6})

f (x) = \frac{- 5 x - 20}{7}

What is the inverse of f(x)=(x^2)/(200)+x/6 ?
The inverse of f(x)=(x^2)/(200)+x/6 is (10(sqrt(18x+25)-5))/3 ,-(10(sqrt(18x+25)+5))/3