What is the inverse of f(x)=ln(arccos(1/(sqrt(x)))) ?

The inverse of f(x)=ln(arccos(1/(sqrt(x)))) is 1/(cos^2(e^x))

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inverse of f(x)=ln(arccos(1/(sqrt(x))))

inverse

f (x) = ln (arccos (\frac{1}{x}))

\frac{1}{cos ^{2} ( e ^{x} )}

Solution steps

Solve for

arccos (\frac{1}{x}), y = ln (arccos (\frac{1}{x}))

arccos (\frac{1}{x}) = e^{y}

arccos (a) = b \Rightarrow a = cos (b)

\frac{1}{x} = cos (e^{y})

Solve for

x, \frac{1}{x} = cos (e^{y})

\frac{1}{cos ^{2} ( e ^{y} )}

Substitute

y = x

\frac{1}{cos ^{2} ( e ^{x} )}

f (x) = (3 - x^{3})^{5}

f (x) = 3 x - 4

2 x - 4

f (x) = x^{2} - 11, x \geq 0

f (x) = \frac{5 x}{x - 4}

What is the inverse of f(x)=ln(arccos(1/(sqrt(x)))) ?
The inverse of f(x)=ln(arccos(1/(sqrt(x)))) is 1/(cos^2(e^x))