For f(x)=6/x and g(x)=6/x, find the following functions.a) (f@g)(x)b) (g@f)(x)c) (f@g)(7)d) (g@f)(7)

opatovaL 2021-02-24 Answered

For f(x)=6/x and g(x)=6/x, find the following functions.

a) (fg)(x)

b) (gf)(x)

c) (fg)(7)

d) (gf)(7)

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Expert Answer

Leonard Stokes
Answered 2021-02-25 Author has 98 answers

a) (fg)(x)=f(g(x))(:(fg)(X)=f(g(x))

=f(6/x)(:g(x)=6/x)
=6/(6/x)(:f(x)=6/x)

=(6x)/6

=x

b) Obtain the composition function g of f as follows.

(gf)(x)=g(f(x))(:(fg)(x)=f(g(x))

=g(6/x)(:g(x)=6/x)

=6/(6/x)(:g(x)=6/x)

=6/6x=x

c) Obtain the value of (fg)(7) as follows.
Substitute for x in (fg)(x)=x

(fg)(7)=7

Thus, the value of (fg)(7) is 7

d) Obtain the value of (gf)(7) as follows.

Substitute for x in (gf)(x)=x

(gf)(7)=7

Thus, the value of (gf)(7) is 7

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