Question

for the given functions f and g, find the composite functions f ∘ g and g ∘ f, and state their domains.

14.

f(x) = 2 /(x-3)

g(x) = 2+x

Answer 1

Given, two functions

f(x) = 2/(x-3) and

g(x) = 2+x

Composite function can be found by applying one given function to the result of another given function.

To find out the composite functions fo g and g o f-

f o g = f [g(x)]

= f[2+x] {putting the value of g(x)}

= 2/ 2+x-3

f o g = 2/ x-1 .....eqⁿ(1)

again, for g o f

g o f = g[f(x)]

= g[ 2/x-3] { putting the value of f(x)}

= 2 + 2/x-3

= 2x-6+2 / x-3

= 2x -4 / x-3

= 2(x-2) / x-3 .....eqn (2)

Above equations are the required answer.