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

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

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inverse of f(x)=(x(x+1))/2

inverse

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

\frac{- 1 + 1 + 8 x}{2}, \frac{- 1 - 1 + 8 x}{2}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{- 1 + 1 + 8 x}{2}, \frac{- 1 - 1 + 8 x}{2}

f (x) = 9 x + 11

f (x) = e^{x} \frac{1}{3 - 2 \cdot e ^{x}}

f (x) = (- 2 x + 2 - 6)

f (x) = ln (2 x - 3) - ln (x + 5) + 1, x = 1

g (x) = (x + 2)^{3}

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