If `f(x)={(x^(2)",","for "x ge1),(x",","for "x lt 0):}`, then fof(x) is given by

Options

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`

Answer

D

Explanation

`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):}`