If $f ( x ) = \frac { x - 3} { x }$ and $g(x) = 5x-4$ , what is the domain of $(f*g)(x)$ ?

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Answer 1 · 2018-03-29T10:44:52

${x inR| x!=4/5}$

First figure out what $(f*g)(x)$ is to do this just put the $g(x)$ function into both of the x spots in $f(x)$

$(f*g)(x)=(5x-4-3)/(5x-4)$ so $(f*g)(x)=(5x-7)/(5x-4)$

We note that for a rational function basically $1/x$ when the denominator is equal to 0 there is no output

So we have to figure out when $5x-4=0$

$5x=4$ so $x=4/5$

So the domain is all the reals apart from $x=4/5$
${x inR| x!=4/5}$

If f ( x ) = \frac { x - 3} { x }f ( x ) = \frac { x - 3} { x } and g(x) = 5x-4g(x) = 5x-4, what is the domain of (f*g)(x)(f*g)(x)?