What is the inverse of f(x)=2cos(3x+2) ?

The inverse of f(x)=2cos(3x+2) is (arccos(x/2)-2)/3

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

inverse

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

\frac{arccos ( \frac{x}{2} ) - 2}{3}

Solution steps

Solve for

cos (3 x + 2), y = 2 cos (3 x + 2)

cos (3 x + 2) = \frac{y}{2}

cos (a) = b \Rightarrow a = arccos (b)

3 x + 2 = arccos (\frac{y}{2})

Solve for

x, 3 x + 2 = arccos (\frac{y}{2})

\frac{arccos ( \frac{y}{2} ) - 2}{3}

Substitute

y = x

\frac{arccos ( \frac{x}{2} ) - 2}{3}

f (x) = - 8 x + 240

y + 1 = \frac{2}{3} (x - 8)

(4, 1), (0, 3)

f (x) = \frac{e ^{x}}{x}

f (x) = \frac{3 x ^{2} - 18 x + 24}{x ^{2} - 4 x}

What is the inverse of f(x)=2cos(3x+2) ?
The inverse of f(x)=2cos(3x+2) is (arccos(x/2)-2)/3