אם f (x) = חטא ^ 3x ו- g (x) = sqrt (3x-1, מה זה f (g (x))?

אם f (x) = חטא ^ 3x ו- g (x) = sqrt (3x-1, מה זה f (g (x))?
Anonim

#f (x) = חטא ^ 3x #, # D_f = RR #

#g (x) = sqrt (3x-1) #, # Dg = 1/3, + oo) #

#D_ (ערפל) = {{# AAx ## in ##RR: ##איקס## in ## D_g #, #g (x) ## in ##D_f} #

#x> = 1/3 #, #sqrt (3x-1) # ## in ## RR # #-># #איקס## in ## 1/3, + oo #

# AAx ## in ## 1/3, + oo #,

  • # (fog) '(x) = f' g (x) g '(x) = f' (sqrt (3x-1)) (3x-1) ') / (2xqrt (3x-1) #

#f '(x) = 3sin ^ 2x (sinx)' = 3sin ^ 2xcosx #

לכן (xx) 1 (x) = חטא = 2 (sqrt (3x-1)) cos (sqrt (3x-1)) 9 / (2sqrt (3x-1)) #