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If f(x)={(x^(2)",","for "x ge0),(x",","...

If `f(x)={(x^(2)",","for "x ge0),(x",","for "x lt 0):}`, then fof(x) is given by

A

`x^(2) " for " x ge 0, x " for " x lt 0`

B

`x^(4) " for " x ge 0, x^(2) " for " x lt 0`

C

`x^(4) " for " x ge 0, -x^(2) " for " x lt 0`

D

`x^(4) " for " x ge 0, x " for " x lt 0`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(f(x))={((f(x))^(2)",", "for " f(x) ge 0),(f(x)",","for " f(x) lt 0):}`
`={((x^(2))^(2)","x^(2) ge 0"," x ge 0),(x^(2)","x ge 0"," x lt 0),(x^(2)"," x^(2) lt 0"," x ge 0),(x"," x lt 0"," x lt 0):}`
`={(x^(4)","x ge 0),(x","x lt 0):}`
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