What is the inverse of f(x)=2x+sqrt(4+x^2) ?

The inverse of f(x)=2x+sqrt(4+x^2) is (2x+sqrt(x^2+12))/3 ,(2x-sqrt(x^2+12))/3

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inverse of f(x)=2x+sqrt(4+x^2)

inverse

f (x) = 2 x + 4 + x^{2}

\frac{2 x + x ^{2} + 12}{3}, \frac{2 x - x ^{2} + 12}{3}

Solution steps

y = 2 x + 4 + x^{2}

Replace

x

with

y

x = 2 y + 4 + y^{2}

Solve for

y, x = 2 y + 4 + y^{2}

\frac{2 x + x ^{2} + 12}{3}, \frac{2 x - x ^{2} + 12}{3}

What is the inverse of f(x)=2x+sqrt(4+x^2) ?
The inverse of f(x)=2x+sqrt(4+x^2) is (2x+sqrt(x^2+12))/3 ,(2x-sqrt(x^2+12))/3