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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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