Question

How do you find (f og)(x) and (g of)(x) given `f(x)=9x-5` and `g(x)=9-3x`?

Answer 1

`(f@g)(x)=76-27x`
`(g@f)(x)=24-27x`

Explanation:

`"Note " (f@g)(x)=f(g(x)" and " (g@f)(x)=g(f(x))`

The method of processing is the same.

`rArrf(g(x))`

`"Substitute g(x) into f(x)"`

`=f(color(red)(9-3x))`

`=9(color(red)(9-3x))-5`

`=81-27x-5`

`=76-27x`

For g( f(x)) substitute f( x) into g( x)

`rArrg(f(x))`

`=g(color(red)(9x-5))`

`=9-3(color(red)(9x-5))`

`=9-27x+15`

`=24-27x`