Math 111 – W8 Written HW Composition & Inverse Ftns Name___________ Due$Thur$W8$ $ $ $ $ $$$$$$$$$Sects$5.1$&$5.2 $Use$the$graph$below$to$answer$the$following$questions.$$You$MUST$use$several$steps$with$appropriate$notation$for$all$of$the$function$compositions!$$1) Evaluate$the$following$compositions$from$the$given$graph.$$You$MUST$use$several$steps$with$appropriate$notation,$as$used$in$class,$for$all$of$the$function$compositions$on$this$HW.$$$a)$$!! f ! g( )(−2) = f g(−2)( )= f (4) = 2$$b)$$!! f ! g( )(3) = f g(3)( )= f (−1)= ?$undefined$$c)$$!! f ! f( )(0) = f f (0)( )= f (0)= 0$$d)$$!! g! f( )(4) = g f (4)( )= g(2) = 0$ $$$$2) What$is$the$domain$of:$$a) !! f ! g( )(x)##!!D = −∞,2(⎤⎦##$b) !! g! f( )(x)#!!D = 0,∞⎡⎣)##$$$3) Use$the$graph$below$to$evaluate$each$of$the$following:$#$ a) f−1(2) = 4b) g−1(−1) = 3c) f−1(−2) = ?? undefinedd)g ! g−1( )(−3) = g g−1(−3)( )= g(5) = −3e)g−1! f−1( )(2) = g−1f−1(2)( )= g−1(4) = −2$Math 111 – W8 Written HW Composition & Inverse Ftns Name___________ Due$Thur$W8$ $ $ $ $ $$$$$$$$$Sects$5.1$&$5.2 $4) Let## #a. Sketch#a#graph#of#h#on#the#axes#at#right.#You#should#be#able#to#graph#it#by#hand#after#studying#rational#functions#last#week,#but#you#can#use#a#graphing#calculator#if#you#need#to.###b. #What#is#the#domain#of#h?##−∞,−32( )∪ −32,∞( )#$c. What#is#the#range#of#h?#Hint#–#you#can#think#about#this#using#the#formula#for#h#or#its#graph!## # # #d. Find#a#symbolic#form#of#1.-h##−∞,−52( )∪ −52,∞( )##h−1(y) =1− 3y2y + 5###$#$$e. Sketch#a#graph#of#1-hon#the#axes#at#right.#Make#sure#to#label#it#as#1.-h#f. What#is#the#domain#of#1?h-##−∞,−52( )∪ −52,∞( )#############$g. What#is#the#range#of#1?h-#−∞,−32( )∪ −32,∞( )###h. How#are#the#domain#and#range#of#a#function#and#its#inverse#are#related?#$Domain$of$h$is$the$range$of$h-inverse$Range$of$h$is$the$domain$of$h-inverse$$$ h(x) =1− 5x2x +