The Function in Exercises 4041 are all onetoone For each fac

The Function in Exercises 40-41 are all one-to-one For each faction Find are equation of f^-1(x) the inverse function.

Solution

solution-

que40

a) f(x)=4x-3= y

(y+3)/4=x

interchange x and y

(x+3)/4=y= f^-1(x)

b) f(f^-1(x))=4[(x+3)/4]3=x

f(f^-1(x))=x

f^-1(f(x))= [(4x-3)+3]/4 =4x/4 = x

f^-1(f(x))=x

que 41

a) f(x)=1/x=y

x=1/y

interchange x and y

y=f^-1(x)=1/x

b)f(f^-1(x))=1/(1/x)=x

f(f^-1(x))=x

f^-1(f(x))=1/(1/x)=x

f^-1(f(x))=x