Question 51335
The notation g(-4) means we take "-4" and substitute it in the g() function anywhere there is "x".  So, {{{g(-4) = 27-9*(-4) = 27-(-36) = 27+36 = 63}}}.  Similarly, for function f(), we get {{{ f(5) = 6*(5)^2 -8*(5) -23 = 6*25 -8*(5)-23 = 150 -8*(5)-23 = 150-40-23=110-23=87}}}.  We do the same for {{{f(5 + h) - f(5)}}}, but have to call the f() function twice:  once for (5+h) and the other for (5).  Solving f(5+h) produces {{{6(5+h)^2 - 8(5+h) - 23}}} which simplifies to {{{6*(h^2+10h+25) -40-8h-23}}}, which further simplifies to {{{6h^2+60h+150-40-8h-23}}}.  Combining like terms produces {{{6h^2+52h+87}}}.  Because we solved f(5) earlier to get {{{f(5)=87}}}, we can now solve {{{f(5 + h) - f(5)}}} by substitution:  {{{6h^2+52h+87-87}}} which simplifies to {{{6h^2+52h}}}, which can be rewritten as {{{2h*(3h+26)}}}.