How do you create an equation using composition using the two equations.. y=0.0979x-2.0363 y=104.24ln(x)-264.22

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to remember what composition of two functions means such that:

`(fog)(x) = f(g(x))`

Supposing that `f(x) = 0.0979x-2.0363 ` and `g(x) = 104.24ln(x)-264.22` , then, using composition yields a new function such that:

`f(g(x)) = 0.0979g(x) -2.0363`

Notice that you need to substitute equation of g(x) for x such that:

`f(g(x)) = 0.0979(104.24ln(x)-264.22) -2.0363`

You need to open brackets such that:

`f(g(x)) = 10.205096ln(x) - 25.867138 - 2.0363`

`f(g(x)) = 10.205096ln(x) - 27.903438`

You may form a new function using composition g of f, `(gof)(x)=g(f(x)) ` such that:

`g(f(x)) = 104.24ln(f(x))-264.22`

`g(f(x)) = 104.24ln(0.0979x-2.0363) - 264.22`

Hence, using composition, you may form two new functions, f of g and g of f, such that `f(g(x)) = 10.205096ln(x) - 27.903438`  and `g(f(x)) = 104.24ln(0.0979x-2.0363) - 264.22` .