Question

Find the function and simplify the function rule.
f(x) = 5x + 1 g(x) = 3x - 4
(f+g)(x) =

Answer 1

(f∘g)(x)=25x-1

(g∘f)(x)=25x+19

Explanation:

To find (f∘g)(x), use the definition of (f∘g)(x),

(f∘g)(x)=f(g(x))

Substituting 5x−1 for g(x) gives

(f∘g)(x)=f(5x−1)

Find f(5x−1), where f(x)=5x+4, and simplify to get

(f∘g)(x)(f∘g)(x)(f∘g)(x)=5(5x−1)+4=25x−5+4=25x−1

To find (g∘f)(x), use the definition of (g∘f)(x),

(g∘f)(x)=g(f(x))

Substituting 5x+4 for f(x) gives

(g∘f)(x)=g(5x+4)

Find g(5x+4), where g(x)=5x−1, and simplify to get

(g∘f)(x)=5(5x+4)−1

(g∘f)(x)=25x+20−1

(g∘f)(x)=25x+19

Answer 2

( f + g )( x ) = 8x - 3

Explanation:

What this is saying is to add the two functions together.

( 5x+1 ) + ( 3x - 4 )

( f + g )( x ) = 8x - 3 is the simplified version.