What is the inverse of f(x)=4sin(pi/2 (x))-1 ?

The inverse of f(x)=4sin(pi/2 (x))-1 is (2arcsin((x+1)/4))/(pi)

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inverse of f(x)=4sin(pi/2 (x))-1

inverse

f (x) = 4 sin (\frac{π}{2} (x)) - 1

\frac{2 arcsin ( \frac{x + 1}{4} )}{π}

Solution steps

Solve for

sin (\frac{π}{2} x), y = 4 sin (\frac{π}{2} x) - 1

sin (\frac{π}{2} x) = \frac{y + 1}{4}

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

\frac{π}{2} x = arcsin (\frac{y + 1}{4})

Solve for

x, \frac{π}{2} x = arcsin (\frac{y + 1}{4})

\frac{2 arcsin ( \frac{y + 1}{4} )}{π}

Substitute

y = x

\frac{2 arcsin ( \frac{x + 1}{4} )}{π}

y = \frac{5 x}{8 x - 3}

y = - x^{2} + 2 x + 3

\frac{5 x - 3}{2 + x}

\frac{s + 1}{s ^{2} - 4 s + 13}

y = \frac{2 x}{3 x - 5}

What is the inverse of f(x)=4sin(pi/2 (x))-1 ?
The inverse of f(x)=4sin(pi/2 (x))-1 is (2arcsin((x+1)/4))/(pi)