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Determine the inverse of this function.

f(x) = 3 cos(2x – 3) + 1

Determine the inverse of this function. f(x) = 3 cos(2x – 3) + 1-example-1
User Drhyde
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1 Answer

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Answer:

a)
f^(-1) (x) = (1)/(2) Cos^(-1) ((x-1)/(3) ) +(3)/(2)

The inverse of given function


f^(-1) (x) = (1)/(2) Cos^(-1) ((x-1)/(3) ) +(3)/(2)

Explanation:

Step(i):-

Given function f(x) = 3 cos (2 x -3) + 1

Let y = f(x) = 3 cos (2 x -3) + 1

y = 3 cos (2 x -3) + 1

⇒ y - 1 = 3 cos (2 x -3)


cos ( 2 x - 3 ) =(y -1)/(3)


cos ^(-1) ( cos (2 x - 3)) = Cos^(-1) ((y-1)/(3) )

We know that inverse trigonometric equations

cos⁻¹(cosθ) = θ


2 x - 3 = Cos^(-1) ((y-1)/(3) )


2 x = Cos^(-1) ((y-1)/(3) ) +3


x = (1)/(2) Cos^(-1) ((y-1)/(3) ) +(3)/(2)

Step(ii):-

we know that y= f(x)

The inverse of the given function


x = f^(-1) (y)


f^(-1) (y) = (1)/(2) Cos^(-1) ((y-1)/(3) ) +(3)/(2)

The inverse of given function in terms of 'x'


f^(-1) (x) = (1)/(2) Cos^(-1) ((x-1)/(3) ) +(3)/(2)

conclusion:-

The inverse of given function


f^(-1) (x) = (1)/(2) Cos^(-1) ((x-1)/(3) ) +(3)/(2)

User Branan
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