What is the inverse of f(x)=4sin(4x+1) ?

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

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inverse of f(x)=4sin(4x+1)

inverse

f (x) = 4 sin (4 x + 1)

\frac{arcsin ( \frac{x}{4} ) - 1}{4}

Solution steps

Solve for

sin (4 x + 1), y = 4 sin (4 x + 1)

sin (4 x + 1) = \frac{y}{4}

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

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

Solve for

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

\frac{arcsin ( \frac{y}{4} ) - 1}{4}

Substitute

y = x

\frac{arcsin ( \frac{x}{4} ) - 1}{4}

(x - 5)^{3} - 3

x^{2} - 7 x + 10

f (x) = \frac{6}{3 x + 5}

f (x) = cos (2 x + 3)

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

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