What is the inverse of ln(arctan(7x^4)) ?

The inverse of ln(arctan(7x^4)) is \sqrt[4]{(tan(e^x))/7},-\sqrt[4]{(tan(e^x))/7}

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inverse of ln(arctan(7x^4))

inverse

ln (arctan (7 x^{4}))

4 \frac{tan ( e ^{x} )}{7}, - 4 \frac{tan ( e ^{x} )}{7}

Solution steps

Solve for

arctan (7 x^{4}), y = ln (arctan (7 x^{4}))

arctan (7 x^{4}) = e^{y}

arctan (a) = b \Rightarrow a = tan (b)

7 x^{4} = tan (e^{y})

Solve for

x, 7 x^{4} = tan (e^{y})

4 \frac{tan ( e ^{y} )}{7}, - 4 \frac{tan ( e ^{y} )}{7}

Substitute

y = x

4 \frac{tan ( e ^{x} )}{7}, - 4 \frac{tan ( e ^{x} )}{7}

f (x) = y^{2} + 2

f (x) = (2 x + 3)

g (x) = \frac{1}{- x - 2}

\frac{2 x + 1}{1 - 4 x}

sin (x^{3})

What is the inverse of ln(arctan(7x^4)) ?
The inverse of ln(arctan(7x^4)) is \sqrt[4]{(tan(e^x))/7},-\sqrt[4]{(tan(e^x))/7}