What is the inverse of (2(x+2)^2)/(x^2) ?

The inverse of (2(x+2)^2)/(x^2) is (2(sqrt(2)sqrt(x)-2))/(2-x),-(2(sqrt(2)sqrt(x)+2))/(-x+2)

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inverse of (2(x+2)^2)/(x^2)

inverse

\frac{2 ( x + 2 ) ^{2}}{x ^{2}}

\frac{2 ( 2 x - 2 )}{2 - x}, - \frac{2 ( 2 x + 2 )}{- x + 2}

Solution steps

y = \frac{2 ( x + 2 ) ^{2}}{x ^{2}}

Replace

x

with

y

x = \frac{2 ( y + 2 ) ^{2}}{y ^{2}}

Solve for

y, x = \frac{2 ( y + 2 ) ^{2}}{y ^{2}}

\frac{2 ( 2 x - 2 )}{2 - x}, - \frac{2 ( 2 x + 2 )}{- x + 2}

4 (x - 1)^{2}

- 2 \cdot 3^{2 x - 1} + 1

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

f (x) = (x + 88)^{2} + 82

f (x) = \frac{x - 5}{x - 4}

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