What is the inverse of f(x)=5x+sqrt(x^2-1) ?

The inverse of f(x)=5x+sqrt(x^2-1) is (5x+sqrt(x^2-24))/(24),(5x-sqrt(x^2-24))/(24)

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inverse of f(x)=5x+sqrt(x^2-1)

inverse

f (x) = 5 x + x^{2} - 1

\frac{5 x + x ^{2} - 24}{24}, \frac{5 x - x ^{2} - 24}{24}

Solution steps

y = 5 x + x^{2} - 1

Replace

x

with

y

x = 5 y + y^{2} - 1

Solve for

y, x = 5 y + y^{2} - 1

\frac{5 x + x ^{2} - 24}{24}, \frac{5 x - x ^{2} - 24}{24}

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

f (x) = \frac{- 4 + 4 x}{- 3 - 3 x}

f (x) = 3 x^{2} + 5 x - 3

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

- 10 x

What is the inverse of f(x)=5x+sqrt(x^2-1) ?
The inverse of f(x)=5x+sqrt(x^2-1) is (5x+sqrt(x^2-24))/(24),(5x-sqrt(x^2-24))/(24)