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

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

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inverse of f(x)=2-sqrt(2)sec(x)

inverse

arcsec (- \frac{2 ( x - 2 )}{2})

Solution steps

Solve for

sec (x), y = 2 - 2 sec (x)

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

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

arcsec (- \frac{2 ( y - 2 )}{2})

Substitute

y = x

arcsec (- \frac{2 ( x - 2 )}{2})

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