If #f(x) = 3x-6# and #g(x) = x-2#, what is #f/g# and its domain?

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Answer 1 · 2017-08-20T20:37:36

See a solution process below:

We can write #(f/g)(x)# as:

#(f/g)(x) = (3x - 6)/(x - 2)#

Factoring the numerator gives:

#(f/g)(x) = ((3 xx x) - (3 xx 2))/(x - 2)#

#(f/g)(x) = (3(x - 2))/(x - 2)#

#(f/g)(x) = (3color(red)(cancel(color(black)((x - 2)))))/color(red)(cancel(color(black)(x - 2)))#

#(f/g)(x) = 3#

The domain of this function is all Real numbers where #(x - 2) != 0# or where #x != 2#