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

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

Question
Composite functions
asked 2021-02-24
For f(x)=6/x and g(x)=6/x, find the following functions. a) ([email protected])(x) b) ([email protected])(x) c) ([email protected])(7) d) ([email protected])(7)

Answers (1)

2021-02-25
a) ([email protected])(x)=f(g(x)) (:'([email protected])(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. ([email protected])(x)=g(f(x))(:'([email protected])(x)=f(g(x)) =g(6/x) (:'g(x)=6/x) =6/(6/x) (:'g(x)=6/x) =6/6*x =x c) Obtain the value of ([email protected])(7) as follows. Substitute for x in ([email protected])(x)=x ([email protected])(7)=7 Thus, the value of ([email protected])(7) is 7 d) Obtain the value of ([email protected])(7) as follows. Substitute for x in ([email protected])(x)=x ([email protected])(7)=7 Thus, the value of ([email protected])(7) is 7
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