What is the inverse of f(x)=sqrt(x^2-x-6) ?

The inverse of f(x)=sqrt(x^2-x-6) is (1+sqrt(4x^2+25))/2 ,(1-sqrt(4x^2+25))/2

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inverse of f(x)=sqrt(x^2-x-6)

inverse

f (x) = x^{2} - x - 6

\frac{1 + 4 x ^{2} + 25}{2}, \frac{1 - 4 x ^{2} + 25}{2}

Solution steps

y = x^{2} - x - 6

Replace

x

with

y

x = y^{2} - y - 6

Solve for

y, x = y^{2} - y - 6

\frac{1 + 4 x ^{2} + 25}{2}, \frac{1 - 4 x ^{2} + 25}{2}

What is the inverse of f(x)=sqrt(x^2-x-6) ?
The inverse of f(x)=sqrt(x^2-x-6) is (1+sqrt(4x^2+25))/2 ,(1-sqrt(4x^2+25))/2