What is the inverse of y= 1/(sqrt(x^2-5x+4)) ?

The inverse of y= 1/(sqrt(x^2-5x+4)) is (5x+sqrt(9x^2+4))/(2x),(5x-sqrt(9x^2+4))/(2x)

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inverse of y= 1/(sqrt(x^2-5x+4))

inverse

y = \frac{1}{x ^{2} - 5 x + 4}

\frac{5 x + 9 x ^{2} + 4}{2 x}, \frac{5 x - 9 x ^{2} + 4}{2 x}

Solution steps

y = \frac{1}{x ^{2} - 5 x + 4}

Replace

x

with

y

x = \frac{1}{y ^{2} - 5 y + 4}

Solve for

y, x = \frac{1}{y ^{2} - 5 y + 4}

\frac{5 x + 9 x ^{2} + 4}{2 x}, \frac{5 x - 9 x ^{2} + 4}{2 x}

f (x) = \frac{5}{x} - 1

f (x) = \frac{5}{x} - 2

f (x) = \frac{2}{π} arcsin (x - 1)

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

f (x) = 3 x^{9} + 6

What is the inverse of y= 1/(sqrt(x^2-5x+4)) ?
The inverse of y= 1/(sqrt(x^2-5x+4)) is (5x+sqrt(9x^2+4))/(2x),(5x-sqrt(9x^2+4))/(2x)