How do you find (f o g)(x) and its domain, (g o f)(x) and its domain, (f o g)(-2) and (g o f)(-2) of the following problem #f(x) = 2x + 3#, #g(x) = 3x -1#?

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Answer 1 · 2017-01-15T10:32:02

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This is a composition of functions.

#f(x)=2x+3#, #=>#, #D_f(x)=RR#

#g(x)=3x-1#, #=>#, #D_g(x)=RR#

#(fog)(x)=f(g(x))=f(3x-1)=2(3x-1)+3#

#=6x-2+3=6x+1#

The domain is #D_(fog)(x)=RR#

#(fog)(-2)=6*-2+1=-11#

#(gof(x))=g(f(x))=g(2x+3)=3(2x+3)-1=6x+9-1=6x+8#

The domain is #D_(gof(x))=RR#

#(gof(-2))=6*-2+8=-4#