What is the inverse of f(x)=sin(4/(5x+2)) ?

The inverse of f(x)=sin(4/(5x+2)) is (4-2arcsin(x))/(5arcsin(x))

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inverse of f(x)=sin(4/(5x+2))

inverse

f (x) = sin (\frac{4}{5 x + 2})

\frac{4 - 2 arcsin ( x )}{5 arcsin ( x )}

Solution steps

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

\frac{4}{5 x + 2} = arcsin (y)

Solve for

x, \frac{4}{5 x + 2} = arcsin (y)

\frac{4 - 2 arcsin ( y )}{5 arcsin ( y )}

Substitute

y = x

\frac{4 - 2 arcsin ( x )}{5 arcsin ( x )}

f (x) = \frac{9 x}{4 x - 1}

f (x) = 4 - x^{2} + 1

\frac{50}{( x + 1 ) ^{2}} + 4

x^{2} + 4 x - 1

x^{2} - 8 x + 4

What is the inverse of f(x)=sin(4/(5x+2)) ?
The inverse of f(x)=sin(4/(5x+2)) is (4-2arcsin(x))/(5arcsin(x))