How do you find the compositions given #f(x)+3x-5# and #g(x)= sqrt(x-2)#?

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Answer 1 · 2016-01-03T16:28:22

#(f@g)(x)=3sqrt(x-2)-5#

#(g@f)(x)=sqrt(3x-7)#

By definition, #(f@g)(x)=f[g(x)]#

#=f(sqrt(x-2))#

#=3sqrt(x-2)-5#.

Similarly, #(g@f)(x)=g[f(x)]#

#=g(3x-5)#

#=sqrt(3x-5-2)#