What is the inverse of f(x)=2cos(3x-5)-4 ?

The inverse of f(x)=2cos(3x-5)-4 is (arccos((x+4)/2)+5)/(3)

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inverse of f(x)=2cos(3x-5)-4

inverse

f (x) = 2 cos (3 x - 5) - 4

\frac{arccos ( \frac{x + 4}{2} ) + 5}{3}

Solution steps

Solve for

cos (3 x - 5), y = 2 cos (3 x - 5) - 4

cos (3 x - 5) = \frac{y + 4}{2}

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

3 x - 5 = arccos (\frac{y + 4}{2})

Solve for

x, 3 x - 5 = arccos (\frac{y + 4}{2})

\frac{arccos ( \frac{y + 4}{2} ) + 5}{3}

Substitute

y = x

\frac{arccos ( \frac{x + 4}{2} ) + 5}{3}

f (7) = 2 (x - 1)

f (x) = (5) (2^{(1 - x)})

\frac{3}{2} x + 12

f (x) = \frac{x + 1}{x + 10}

ln (4)

What is the inverse of f(x)=2cos(3x-5)-4 ?
The inverse of f(x)=2cos(3x-5)-4 is (arccos((x+4)/2)+5)/(3)