case a) f(x)=[x-1]/[x+5] step 1 f(x)=y y=[x-1]/[x+5] step 2 exchange x for y and y for x y=[x-1]/[x+5]------> x=[y-1]/[y+5]----> x*[y+5]=[y-1]----> xy+5x=y-1 step 3 clear the variable y xy+5x=y-1-----> y-xy=5x+1----> y*[1-x]=[5x+1]----> y=[5x+1]/[1-x] step 4 f(x)-1= [5x+1]/[1-x] the function and the inverse function are not the same
case b) g(x)=[x-2]/[x-1] step 1 g(x)=y y=[x-2]/[x-1] step 2 exchange x for y and y for x y=[x-2]/[x-1]------> x=[y-2]/[y-1]----> x*[y-1]=[y-2]----> xy-x=y-2 step 3 clear the variable y xy-x=y-2-----> xy-y=-2+x----> y*[x-1]=[x-2]----> y=[x-2]/[x-1] step 4 g(x)-1= [x-2]/[x-1] the function and the inverse function are the same
case c) h(x)=[x+3]/[x-2] step 1 h(x)=y y=[x+3]/[x-2] step 2 exchange x for y and y for x y=[x+3]/[x-2]------> x=[y+3]/[y-2]----> x*[y-2]=[y+3]----> xy-2x=y+3 step 3 clear the variable y xy-2x=y+3-----> xy-y=3+2x----> y*[x-1]=[2x+3]----> y=[2x+3]/[x-1] step 4 h(x)-1= [2x+3]/[x-1] the function and the inverse function are not the same
case d) k(x)=[x+1]/[x-1] step 1 k(x)=y y=[x+1]/[x-1] step 2 exchange x for y and y for x y=[x+1]/[x-1]------> x=[y+1]/[y-1]---> x*[y-1]=[y+1]----> xy-x=y+1 step 3 clear the variable y xy-x=y+1-----> xy-y=x+1----> y*[x-1]=[x+1]----> y=[x+1]/[x-1] step 4 k(x)-1= [x+1]/[x-1] the function and the inverse function are the same
