What is the inverse of f(x)=5arcsin(x^3) ?

The inverse of f(x)=5arcsin(x^3) is cube root of sin(x/5)

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inverse of f(x)=5arcsin(x^3)

inverse

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

3 sin (\frac{x}{5})

Solution steps

Solve for

arcsin (x^{3}), y = 5 arcsin (x^{3})

arcsin (x^{3}) = \frac{y}{5}

arcsin (a) = b \Rightarrow a = sin (b)

x^{3} = sin (\frac{y}{5})

Solve for

x, x^{3} = sin (\frac{y}{5})

3 sin (\frac{y}{5})

Substitute

y = x

3 sin (\frac{x}{5})

l in e (213, 0), (250, 1.1 \cdot 1 0^{5})

d o main f (x) = 3 x^{2} + 2 x - 4

in t erce pt s x^{2} + 4 x - 5

l in e (- 2, - 5), (6, - 5)

d o main 3 - x^{2} - 16

What is the inverse of f(x)=5arcsin(x^3) ?
The inverse of f(x)=5arcsin(x^3) is cube root of sin(x/5)