What is the inverse of f(x)=((sin(x+1)))/3 ?

The inverse of f(x)=((sin(x+1)))/3 is arcsin(3x)-1

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inverse of f(x)=((sin(x+1)))/3

inverse

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

arcsin (3 x) - 1

Solution steps

Solve for

sin (x + 1), y = \frac{sin ( x + 1 )}{3}

sin (x + 1) = 3 y

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

x + 1 = arcsin (3 y)

Solve for

x, x + 1 = arcsin (3 y)

arcsin (3 y) - 1

Substitute

y = x

arcsin (3 x) - 1

f (x) = f (a) = - 4 a^{2} - 3

f (x) = \frac{7 x - 1}{2 x + 5}

f (x) = 3 - ln (x + 2)

f (x) = \frac{100}{x - 12} + 8

y = e^{x} + 2

What is the inverse of f(x)=((sin(x+1)))/3 ?
The inverse of f(x)=((sin(x+1)))/3 is arcsin(3x)-1