Diketahui . Jika g(x) = f(2x - 1), maka g turun pada selang ...

Diketahui $begin mathsize 12px style f open parentheses x close parentheses equals 2 over 3 x cubed minus 1 half x squared minus 3 x plus 1 over 6 end style$ . Jika g(x) = f(2x - 1), maka g turun pada selang ...

$begin mathsize 12px style negative 5 over 4 less or equal than x less or equal than 1 end style$
$begin mathsize 12px style 0 less or equal than x less or equal than 5 over 4 end style$
$begin mathsize 12px style negative 1 less or equal than x less or equal than 1 end style$
$begin mathsize 12px style negative 1 less or equal than x less or equal than 0 end style$
$begin mathsize 12px style 0 less or equal than x less or equal than 1 end style$

Jawaban:

Diketahui $undefined$ dan g(x) = f(2x - 1), maka:

$begin mathsize 12px style g open parentheses x close parentheses equals 2 over 3 open parentheses 2 x minus 1 close parentheses cubed minus 1 half open parentheses 2 x minus 1 close parentheses squared minus 3 open parentheses 2 x minus 1 close parentheses plus 1 over 6 end style$

Kurva turun ketika turun pertamanya kurang dari sama dengan 0, yaitu:

$begin mathsize 12px style g apostrophe open parentheses x close parentheses less or equal than 0 g apostrophe open parentheses x close parentheses equals 4 open parentheses 2 x minus 1 close parentheses squared minus 2 open parentheses 2 x minus 1 close parentheses minus 6 4 open parentheses 4 x squared minus 4 x plus 1 close parentheses minus 4 x plus 2 minus 6 equals 0 16 x squared minus 16 x plus 4 minus 4 x minus 4 equals 0 bottom enclose 16 x squared minus 20 x equals 0 end enclose space space left parenthesis colon space 4 right parenthesis 4 x squared minus 5 x equals 0 x open parentheses 4 x minus 5 close parentheses equals 0 end style$

x = 0 atau x = $begin mathsize 12px style 5 over 4 end style$ (pembuat nol)

Jadi, g(x) akan turun pada selang $begin mathsize 12px style 0 less or equal than x less or equal than 5 over 4 end style$

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