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

The inverse of f(x)=sec^2(x) is arcsec(sqrt(x)),arcsec(-sqrt(x))

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inverse of f(x)=sec^2(x)

inverse

f (x) = sec^{2} (x)

arcsec (x), arcsec (- x)

Solution steps

Solve for

sec (x), y = sec^{2} (x)

sec (x) = y, sec (x) = - y

sec (a) = b \Rightarrow a = arcsec (b)

arcsec (y), arcsec (- y)

Substitute

y = x

arcsec (x), arcsec (- x)

f (x) = 3 - (x + 1)^{2}

\frac{4 x ^{2} - 1}{5 - 7 x ^{2}}

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

f (x) = - \frac{x - 2}{6}

What is the inverse of f(x)=sec^2(x) ?
The inverse of f(x)=sec^2(x) is arcsec(sqrt(x)),arcsec(-sqrt(x))