Question 116014
c)




{{{g(x)=ln(t+4)}}} Start with the given function


Remember you cannot take the log of a negative value or of zero. So that means the argument {{{t+4}}} must be greater than zero (i.e. the argument <font size=4><b>must</b></font> be positive)


{{{t+4>0}}} Set the inner expression greater than zero


{{{t>0-4}}}Subtract 4 from both sides



{{{t>-4}}} Combine like terms on the right side



So that means t must be greater than -4

So here is the domain in interval notation: (-4,*[Tex \LARGE \infty])



Notice if we graph {{{g(x)=ln(t+4)}}}  (just replace t with x), we get

{{{ graph( 500, 500, -10, 10, -10, 10, ln(x+4)) }}} notice how the graph never crosses the line {{{x=-4}}}. So this graphically verifies our answer.