Question 1178519


Find the domain of the composite function f∘g.

{{{f(x) = x + 6}}}
{{{g(x) = 2/(x+7)}}}

{{{f}}}∘{{{g}}}={{{f(g(x))}}}

{{{f}}}∘{{{g}}}={{{f(2/(x+7))}}}

{{{f}}}∘{{{g}}}={{{2/(x+7)+6}}}

domain:

{{{x}}} is in denominator and denominator cannot be equal to zero, so exclude

{{{x+7=0}}}
{{{x=-7}}}

and domain is

{ {{{x}}} element{{{ R}}} :{{{ x<>-7}}} }


{{{ graph( 600, 600, -10, 10, -10, 10, 2/(x+7)+6) }}}