What is the inverse of f(x)=2x^2-1/4 ?

The inverse of f(x)=2x^2-1/4 is (sqrt(2)sqrt(4x+1))/4 ,-(sqrt(2)sqrt(4x+1))/4

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inverse of f(x)=2x^2-1/4

inverse

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

\frac{2 4 x + 1}{4}, - \frac{2 4 x + 1}{4}

Solution steps

y = 2 x^{2} - \frac{1}{4}

Replace

x

with

y

x = 2 y^{2} - \frac{1}{4}

Solve for

y, x = 2 y^{2} - \frac{1}{4}

\frac{2 4 x + 1}{4}, - \frac{2 4 x + 1}{4}

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