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Find f(x) when it is given by f(x)=max...

Find f(x) when it is given by
`f(x)=max{x^(3),x^(2),(1)/(64)},AA x in [0, oo).`

A

`f(x)={(x^(2)",",0 le x le 1),(x^(3)",", x gt 1):}`

B

`f(x)={((1)/(64)",",0 le x le (1)/(4)),(x^(2)",", (1)/(4) lt x le 1),(x^(3)",", x gt 1):}`

C

`f(x)={((1)/(64)",",0 le x le (1)/(8)),(x^(2)",", (1)/(8) lt x le 1),(x^(3)",", x gt 1):}`

D

`f(x)={((1)/(64)",",0 le x le (1)/(8)),(x^(3)",", x gt 1//8):}`

Text Solution

Verified by Experts

The correct Answer is:
C

Clearly, from the graph, `f(x)={((1)/(64)",",0 le x le (1)/(8)),(x^(2)",", (1)/(8) lt x le 1),(x^(3)",", x gt 1):}`
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