What is the inverse of f(x)=x(x/2+0.5) ?

The inverse of f(x)=x(x/2+0.5) is -0.5+sqrt(0.25+2x),-0.5-sqrt(0.25+2x)

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inverse of f(x)=x(x/2+0.5)

inverse

f (x) = x (\frac{x}{2} + 0.5)

- 0.5 + 0.25 + 2 x, - 0.5 - 0.25 + 2 x

Solution steps

y = x (\frac{x}{2} + 0.5)

Replace

x

with

y

x = y (\frac{y}{2} + 0.5)

Solve for

y, x = y (\frac{y}{2} + 0.5)

- 0.5 + 0.25 + 2 x, - 0.5 - 0.25 + 2 x

3 x \frac{1}{4 x} 1

f (x) = 15 x^{2} - 1

f (x) = (x + 2)^{3} + 7

f (x) = 15 x^{2} + 1

f (x) = 15 x^{2} + 7

What is the inverse of f(x)=x(x/2+0.5) ?
The inverse of f(x)=x(x/2+0.5) is -0.5+sqrt(0.25+2x),-0.5-sqrt(0.25+2x)