Question

[HELP 98 POINTS!]
19 ,20

Answer 1

19. ans is f(x) = 9/x + 2 and g(x)= x^2

y=f(g(x))=f(x^2)=9/x^2 + 2

20. alternate proof:

f(x)=9x+3

so y=9x+3

9x=y-3

x=(y-3)/9

swapping x <=> y

y=(x-3)/9=g(x)

so f and g are inverses

Answer 2

19 is easy:

f(x) = 9/x + 2

g(x)= x^2

f(g(x)) = f(x^2) = 9/x^2 + 2

so y = f(g(x)) = 9/x^2 + 2

20. f(x)=9x+3

g(x)=(x-3)/9

f(g(x))=f((x-3)/9=9((x-3)/9)+3

=(x-3)+3

=x

g(f(x))=g(9x+3)=((9x+3)-3)/9

=9x/9

=x