Question

For the following problems, find the function f ° g and the domain of f ° g .

2) f(x) =

`(x)/(x + 4)`
;

`g(x) = (16)/(x + 2)`


3) f(x) =

`√(x)`
; g(x)= 5x+5

Answer 1

`2)\\f(x)=(x)/(x+4)\\\\g(x)=(16)/(x+2)\\\\Domain:\\\\D_f:x\\eq-4\\\\D_g:x\\eq-2\\\\(f\ \circ\ g)(x)=((x)/(x+4))/((16)/(x+2))=(x)/(x+4)\cdot(x+2)/(16)=(x^2+2x)/(16x+64)\\\\Domain:\\\\16x+64\\eq0\to16x\\eq-64\to\boxed{x\\eq-4}`

`3)\\f(x)=√(x)\\\\g(x)=5x+5\\\\Domain:\\\\D_f:x\geq0\\\\D_g:x\in\mathbb{R}\\\\(f\ \circ\ g)(x)=√(5x+5)\\\\Domain:\\\\5x+5\geq0\to5x\geq-5\to\boxed{x\geq-1}`