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

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

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

inverse

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

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

Solution steps

y = 5 x^{2} - 2

Replace

x

with

y

x = 5 y^{2} - 2

Solve for

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

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

f (x) = 8 x^{2} - 50

f (x) = \frac{( x + 3 )}{( x + 2 )}

\frac{x - 7}{x - 49}

\frac{x + 5}{x + 8}

f (x) = 6 (ln (x) - 4)

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