Question

Find f o g, g o f, and g o g.
f(x) = -5x,
g(x) = x + 3

Answer 1

f o g = -3, g o f = 5\3,g o g = -3

Explanation:

for f o g,

f(x+3)

-5(x+3)

-5x-15

or,5x= -15

x = -15\5

therefore x =-3

for g o f,

g(-5x)

-5x+3

or,5x=3

or,x=5\3

for g o g,

g(x+3)

(x+3)3

3x+9

or, -3x =9

or, x=9\ -3

x= -3

Answer 2

see explanation

Explanation:

to obtain f ￮ g , substitute x = g(x) into f(x) , that is

f(g(x))

= f(x + 3)

= - 5(x + 3)

= - 5x - 15

----------------------------

to obtain g ￮ f , substitute x = f(x) into g(x) , that is

g(f(x))

= g(- 5x)

= - 5x + 3

----------------------------

to obtain g ￮ g , substitute x = g(x) into g(x) , that is

g(g(x))

= g(x + 3)

= x + 3 + 3

= x + 6