What is the general solution for solvefor x,f^{-1}=arctan(x^3-1) ?

The general solution for solvefor x,f^{-1}=arctan(x^3-1) is x=\sqrt[3]{tan(1/f)+1}

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solvefor x,f^{-1}=arctan(x^3-1)

solve for

x, f^{- 1} = arctan (x^{3} - 1)

Solution steps

f^{- 1} = arctan (x^{3} - 1)

Switch sides

arctan (x^{3} - 1) = f^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

arctan (x^{3} - 1) = \frac{1}{f}

Apply trig inverse properties

arctan (x^{3} - 1) = \frac{1}{f}

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

x^{3} - 1 = tan (\frac{1}{f})

x^{3} - 1 = tan (\frac{1}{f})

Solve

x^{3} - 1 = tan (\frac{1}{f})

Move

1

to the right side

x^{3} - 1 = tan (\frac{1}{f})

Add

1

to both sides

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

Simplify

x^{3} = tan (\frac{1}{f}) + 1

x^{3} = tan (\frac{1}{f}) + 1

For

x^{n} = f (a)

, n is odd, the solution is

3 cos (B) + 3 = 0

sin (2 θ) = \frac{3}{4}

sin^{2} (x) = 2 \cdot sin (x) + 3

3 tan (θ) + 2 cos (θ) = 0

9 + cot^{2} (x) = 12

What is the general solution for solvefor x,f^{-1}=arctan(x^3-1) ?
The general solution for solvefor x,f^{-1}=arctan(x^3-1) is x=\sqrt[3]{tan(1/f)+1}