What is the inverse of f(x)=9arcsin(-1/2 x) ?

The inverse of f(x)=9arcsin(-1/2 x) is -2sin(x/9)

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inverse of f(x)=9arcsin(-1/2 x)

inverse

f (x) = 9 arcsin (- \frac{1}{2} x)

- 2 sin (\frac{x}{9})

Solution steps

Solve for

arcsin (- \frac{1}{2} x), y = 9 arcsin (- \frac{1}{2} x)

arcsin (- \frac{1}{2} x) = \frac{y}{9}

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

- \frac{1}{2} x = sin (\frac{y}{9})

Solve for

x, - \frac{1}{2} x = sin (\frac{y}{9})

- 2 sin (\frac{y}{9})

Substitute

y = x

- 2 sin (\frac{x}{9})

\frac{3}{4} x + 12

f (x) = (x + 10)^{2}

x - x^{2}

f (x) = 2^{5 x + 7}

f (x) = 2 (x - 0.75) - 2.125

What is the inverse of f(x)=9arcsin(-1/2 x) ?
The inverse of f(x)=9arcsin(-1/2 x) is -2sin(x/9)