What is the inverse of f(x)= 1/9 (2x(x+1)-x-10)+1 ?

The inverse of f(x)= 1/9 (2x(x+1)-x-10)+1 is (-1+3sqrt(8x+1))/4 ,(-1-3sqrt(8x+1))/4

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inverse of f(x)= 1/9 (2x(x+1)-x-10)+1

inverse

f (x) = \frac{1}{9} (2 x (x + 1) - x - 10) + 1

\frac{- 1 + 3 8 x + 1}{4}, \frac{- 1 - 3 8 x + 1}{4}

Solution steps

y = \frac{1}{9} (2 x (x + 1) - x - 10) + 1

Replace

x

with

y

x = \frac{1}{9} (2 y (y + 1) - y - 10) + 1

Solve for

y, x = \frac{1}{9} (2 y (y + 1) - y - 10) + 1

\frac{- 1 + 3 8 x + 1}{4}, \frac{- 1 - 3 8 x + 1}{4}

f (x) = 5 x^{5} - 9

f (x) = \frac{( 1 + e ^{- x} )}{5 e ^{x}}

f (x) = \frac{1}{x ^{2} - 5}

f (x) = 5 - 2 x

y = \frac{5}{4} x - 7

What is the inverse of f(x)= 1/9 (2x(x+1)-x-10)+1 ?
The inverse of f(x)= 1/9 (2x(x+1)-x-10)+1 is (-1+3sqrt(8x+1))/4 ,(-1-3sqrt(8x+1))/4