Answer to Question #235353 in Calculus for CCW

Question #235353
  1. (3.) Using the definition of an inverse, are f(x) and g(x) inverses of one another? Why or why not?
1
Expert's answer
2021-09-13T07:54:26-0400

Let consider these function

Let


f(x)=x+32f(x)=\frac{x+3}{2}


g(x)=2x3g(x)=2x-3

If function f(x)f(x) and g(x)g(x) are inverses, their composition will equal xx


Composition 1:

f(g(x))=f(x)=(2x+3)+32=2x2=xf(g(x))=f(x)=\frac{(2x+3)+3}{2}=\frac{2x}{2}=x


Composition 2:

g(f(x))=2(x+32)3=x+33=xg(f(x)) =2(\frac{x+3}{2})-3=x+3-3=x


Hence these are inverse as their compositions equal x.





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