How do you find the domain and range of $g(x)=7/(7-6x)$ ?

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Answer 1 · 2016-06-25T19:39:56

Domain of $g$ is $RR-{7/6}.$

Range of $g$ is $RR-{0}.$

Division by zero is not permitted, so, fun. $g$ will be undefined when $7-6x=0,$ i.e., when $x=7/6.$

So, Domain of $g$ is $RR-{7/6}.$

Also, notice that, $AA x in RR-{7/6}, g(x)!=0,$ bcz. $g(x)=0 rArr 7/(7-6x)=0 rArr 7=0,$ an impossible result.

Hence, $AA x in RR-{7/6}, g(x)!=0,$ meaning that the Range of $g$ is $RR-{0}.$

How do you find the domain and range of g(x)=7/(7-6x)g(x)=7/(7-6x)?