What is the inverse of f(x)= pi/3+2arcsin(1+2x) ?

The inverse of f(x)= pi/3+2arcsin(1+2x) is (sin((3x-pi)/6)-1)/(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse of f(x)= pi/3+2arcsin(1+2x)

inverse

f (x) = \frac{π}{3} + 2 arcsin (1 + 2 x)

\frac{sin ( \frac{3 x - π}{6} ) - 1}{2}

Solution steps

Solve for

arcsin (1 + 2 x), y = \frac{π}{3} + 2 arcsin (1 + 2 x)

arcsin (1 + 2 x) = \frac{3 y - π}{6}

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

1 + 2 x = sin (\frac{3 y - π}{6})

Solve for

x, 1 + 2 x = sin (\frac{3 y - π}{6})

\frac{sin ( \frac{3 y - π}{6} ) - 1}{2}

Substitute

y = x

\frac{sin ( \frac{3 x - π}{6} ) - 1}{2}

f (x) = \frac{7 x - 8}{3}

4 x^{2} - x + 17

f (x) = \frac{2 y - 5}{3 y}

f (x) = (x + 7)^{3} - 13

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

What is the inverse of f(x)= pi/3+2arcsin(1+2x) ?
The inverse of f(x)= pi/3+2arcsin(1+2x) is (sin((3x-pi)/6)-1)/(2)