Given the functions $g(x) = 3/(x - 1)$ , $f(x) = (x - 1)/(x - 3)$ what is g(f(x))?

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Answer 1 · 2015-12-11T04:03:28

$(3x-9)/2$

To find $g(f(x))$ , take $f(x)$ , or $color(blue)((x-1)/(x-3))$ , and plug it in for $x$ in $g(x)$ , or $3/(color(blue)(x)-3)$ .

You get that

$g(f(x))=3/(color(blue)((x-1)/(x-3))-1)$

Multiply everything by $x-3$ .

$=3/((x-1)/(x-3)-1)((x-3)/(x-3))=(3(x-3))/((x-1)-1(x-3))$

$=(3(x-3))/(x-1-x+3)=(3x-9)/2$

Given the functions g(x) = 3/(x - 1)g(x) = 3/(x - 1), f(x) = (x - 1)/(x - 3)f(x) = (x - 1)/(x - 3) what is g(f(x))?