Question

If f(x)=3x-1 and g(x)=x+5, find (f o g)(x) and (g o f)(x)

(f o g)(x)=

(g o f)(x)

Answer 1

(f o g)(x)= 3x + 14

(g o f)(x) = 3x + 4

Explanation:

(f o g)(x) = f(g(x)) = f(x + 5) = 3(x + 5) - 1 = 3x + 15 - 1 = 3x + 14

(g o f)(x) = g(f(x)) = g(3x - 1) = 3x - 1 + 5 = 3x + 4

Answer 2

`(f \circ g)(x) = 3x + 14`

`(g \circ f)(x) = 3x + 4`

Explanation:

Hello!

Rewrite the equations:

• 
  `(f \circ g)(x) = f(g(x))`
• 
  `(g \circ f)(x) = g(f(x))`

Given that:

• f(x) = 3x - 1
• g(x) = x + 5

Solve for
`(f \circ g)(x)`:

• 
  `f(g(x)) = 3(g(x)) - 1`

• 
  `f(x + 5) = 3(x + 5) - 1`

• 
  `f(x + 5) = 3x + 15 - 1`
• 
  `f(x + 5) = 3x + 14`

`(f \circ g)(x) = 3x + 14`

Solve for
`(g \circ f)(x)`:

• 
  `g(f(x)) = f(x) + 5`
• 
  `g(3x - 1) = (3x - 1) + 5`
• 
  `g(3x - 1) = 3x +4`

`(g \circ f)(x) = 3x + 4`