Question

Using f(x) = 5x + 4 and g(x) = x - 3,find: 1. f(g(6)) 2. g(f(-7)) 3. f(f(8)) 4. g(f(x))

Answer 1

Answer:

Part 1):

• $f(g(6))=19$

Part 2):

• $g(f(-7))=-34$

Part 3):

• $f(f(8))=224$

Part 4):

• $g(f(x))=5x+1$

Step-by-step explanation:

Considering the function

$f(x) = 5x + 4$

$g(x) = x - 3$

Part 1)

To evaluate $f(g(6))$, you must find $g(6)$

so

$g(x) = x - 3$

Put x = 6

$g(6) = 6 - 3$

$g(6) = 3$

Then  

$f(g(6))=f(3)$

$=5(3)+4$

$=19$

Therefore, $f(g(6))=19$

Part 2)

To evaluate $g(f(-7))$, you must find $f(-7)$

so

$f(x) = 5x + 4$

Put x = -7

$f(-7) = 5(-7) + 4$

$=-35+4$

$=-31$

Then  

$g(f(-7))=g(-31)$

$= (-31) - 3$

$=-34$

Therefore, $g(f(-7))=-34$

Part 3)

To evaluate $f(f(8))$, you must find $f(8)$

$f(x) = 5x + 4$

Put x = 8

$f(8)=5(8)+4=40+4=44$

Then

$f(f(8))=f(44)=5(44)+4=220+4=224$

Therefore,

$f(f(8))=224$

Part 4)

Evaluate

$g(f(x))$

As

$f(x) = 5x + 4$

$g(x) = x - 3$

so

$g(f(x))=g(5x+4)$

            $=(5x+4)-3$

            $=5x+4-3$

            $=5x+1$

Therefore,

$g(f(x))=5x+1$