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  • Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 21 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 21 Maths Textbook Solution.

Answers (1)

Answer:

                f is not invertible

Given:

                f\left ( x \right )= \cos \left ( x+2 \right )
Hint:
If the function is invertible, that should fulfil the one-one, onto condition.
Solution:
Let x,y be two elements in the domain \left ( R \right )

                f\left ( x \right )= f\left ( y \right )

                \cos \left ( x+2 \right )=\cos \left ( y+2 \right )

                \left ( x+2 \right )=2\pi - \left ( y+2 \right )

                x=2\pi -y-4

So, we can’t say x=y

For example,

                \cos \frac{\pi }{2}= \cos \frac{3\pi }{2}=0

So, \frac{\pi }{2} and \frac{3\pi }{2}=0

So, \frac{\pi }{2} and \frac{3\pi }{2} have the same image 0

f is not one-one, bijection, surjection.

Hence, f is not invertible.

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