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

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

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

inverse

f (x) = \frac{2}{π} arcsin (x - 1)

sin (\frac{x π}{2}) + 1

Solution steps

Solve for

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

arcsin (x - 1) = \frac{y π}{2}

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

x - 1 = sin (\frac{y π}{2})

Solve for

x, x - 1 = sin (\frac{y π}{2})

sin (\frac{y π}{2}) + 1

Substitute

y = x

sin (\frac{x π}{2}) + 1

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