What is the inverse of f(x)=2arcsec(sqrt(x)) ?

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

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inverse of f(x)=2arcsec(sqrt(x))

inverse

f (x) = 2 arcsec (x)

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

Solution steps

Solve for

arcsec (x), y = 2 arcsec (x)

arcsec (x) = \frac{y}{2}

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

x = sec (\frac{y}{2})

Solve for

x, x = sec (\frac{y}{2})

sec^{2} (\frac{y}{2})

Substitute

y = x

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

f (x) = 6 - \frac{5 x}{3}

f (x) = 5 + 3 x - 1

2 x + 64

f (x) = x^{2} + 6 x + 5

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

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