Question 54175
rop(x) means r composite p of x.  It means that you put the p function everywhere there's an x in the r function.
{{{p(x)=x^2-x-5}}}
{{{r(x)=2x-1}}}
{{{rop(x)=r(x^2-x-5)}}}
{{{r(x^2-x-5)=2(x^2-x-5)-1}}}
{{{r(x^2-x-5)=2x^2-2x-10-1}}}
{{{r(x^2-x-5)=2x^2-2x-11}}}
{{{rop(x)=2x^2-2x-11}}}
Because you need to find rop(6) substitute 6 in for the x in the composite function.
{{{rop(6)=2(6)^2-2(6)-11}}}
{{{rop(6)=2(36)-2(6)-11}}}
{{{rop(6)=72-12-11}}}
{{{highlight(rop(6)=49)}}}
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Another way to do it is to find p(6) and then substitute that answer into r(x).
{{{p(6)=(6)^2-6-5}}}
{{{p(6)=36-6-5}}}
{{{p(6)=25}}}
{{{r(25)=2(25)-1}}}
{{{r(25)=50-1}}}
{{{r(25)=49}}}
Therefore {{{highlight(rop(6)=49)}}}
Happy Calculating!!!