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

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

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

inverse

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

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

f (x) = - 30 x^{2} + 28 x - 6

f (x) = \frac{x - 3}{x ^{2} - 4}

\frac{36}{x ^{2}}

f (x) = \frac{16 x ^{2}}{x ^{4} + 64}

f (x) = \frac{2 x - 16}{5}

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