Question

The function f is such that f(x) = 2x/3x+5 The function g is such that g(x) = 3/x+4 Find fg(-5)

Answer 1

`f(g(-5)) = (3)/(2)`

Explanation:

Given

`f(x) = (2x)/(3x+5)`

`g(x) = (3)/(x+4)`

Required

Find f(g(-5))

First, we calculate f(g(x))

`f(x) = (2x)/(3x+5)`

Substitute g(x) for x

`f(g(x)) = (2g(x))/(3g(x) + 5)`

Substitute
`(3)/(x+4)` for g(x)

`f(g(x)) = (2*(3)/(x+4))/(3*(3)/(x+4) + 5)`

`f(g(x)) = ((6)/(x+4))/((9)/(x+4) + 5)`

`f(g(x)) = (6)/(x+4)/ ((9)/(x+4) + 5})`

Take LCM

`f(g(x)) = (6)/(x+4)/ (9+5x+20)/(x+4)}`

`f(g(x)) = (6)/(x+4)/ (5x+29)/(x+4)}`

Rewrite as multiplication

`f(g(x)) = (6)/(x+4)* (x+4)/(5x+29)}`

`f(g(x)) = (6)/(5x+29)`

Substitute -5 for x

`f(g(-5)) = (6)/(-5*5+29)`

`f(g(-5)) = (6)/(-25+29)`

`f(g(-5)) = (6)/(4)`

`f(g(-5)) = (3)/(2)`