Let f minus 6 6 rarr R be defined by f x x2 minus 3 Consider the following 1 f deg f deg f minus 1 f...........

Mathematics (NDA) Relations and Functions

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Let f:[−6,6]→R be defined by f(x)=x²−3.Consider the following:

1.(f°f°f)(−1)=(f°f°f)(1)

2. (f°f°f)(−1)−4(f°f°f)(1)=(f°f)(0)

Which of the above is/are correct?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

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Explanation:

f(x) = x ² – 3
f o f (x) = (x ² – 3) ²–3 = x ⁴ – 6x ² + 6
f o f o f (x) = (x ⁴ – 6x ² + 6) ² – 3
f o f o f (x) is even function
=> (f o f o f) (–1) = (f o f o f ) (1)
Next (f o f o f) (–1) –4 (f o f o f) (1)
–3 {(f o f o f) (1)} = (–3) (–2) = 6
f o f (o) = 6
Both 1 and 2 are correct