501 MrG What's an Inverse Function?

2548 days ago by MATH4R2013

#1) find the inverse of y==x^3 var('y') equ=x==y^3;show(equ) equ=equ^(1/3);show(equ.simplify_radical()) plot([x^3,x,x^(1/3)],0,2,aspect_ratio=1) 
       


#2)show that f(x) and g(x) are inverses iff f(x)=3*x and g(x)=x/3 f(x)=3*x;show(f(x)) g(x)=x/3;show(g(x)) show(f(g(x))) plot([f(x),x,g(x)],-4,2,aspect_ratio=1) 
       



#3)show that f(x) and g(x) are inverses iff f(x)=2*x+3 and g(x)=(x-3)/2 f(x)=2*x+3;show(f(x)) g(x)=(x-3)/2;show(g(x)) show(f(g(x))) plot([f(x),x,g(x)],-4,2,aspect_ratio=1) 
       



#4)show that f(x) and g(x) are inverses iff f(x)=2*x+3 and g(x)=(x-3)/2 f(x)=2*x+3;show(f(x)) g(x)=(x-3)/2;show(g(x)) show(f(g(x))) plot([f(x),x,g(x)],-4,2,aspect_ratio=1) 
       
#5)show that f(x) and g(x) are inverses #5)iff f(x)=(2*x+1)/(x-1) and g(x)=(x+1)/(x-2) f(x)=(2*x+1)/(x-1);show(f(x)) g(x)=(x+1)/(x-2);show(g(x)) show(f(g(x)).simplify_rational()) p1=plot([f(x)],-3,.9,color='red') p2=plot([g(x)],-3,.9,color='green') p3=plot([x],-3,.9) p4=plot([f(x)],2.1,6,color='red') p5=plot([g(x)],2.1,6,color='green') p6=plot([x],2.1,6) show(p1+p2+p3+p4+p5+p6,aspect_ratio=1)