Question

Please help me with this also jjodlask​

Answer 1

Composite functions

When a function is substituted into another function it is known as a composite function.

Given the following functions:

f(x) = 4x  + 3

g(x) = x - 2

Determine $f(g(x)) \ and \ g(f(x))$

$f(g(x)) = f(x-2)\\ f(x-2) = 4(x-2)+3\\ f(x-2)=4x-8+3\\ f(x-2) = 4x - 5\\ f(g(x)) = 4x - 4$

1) Determine the value of $f(g(5))$

$f(g(5))=4(5) - 4\\ f(g(5))=20-4\\ f(g(5))=16$

2) For the function $g(f(-6))$

$g(f(-6))=4(-6) + 1\\ g(f(-6))=-24+1\\ g(f(-6))=-23$

3) For the value $f(f(7)),$we need to determine $f(f(x))$

$f(f(x)) = f(4x+3)\\ f(f(x))= 4(4x+3)+3\\ f(f(x))=16x+12+3\\ f(f(x))=16x+15\\ f(f(7)) = 16(7) + 15\\ f(f(7)) = 127$

4) For the function $g(f(x));$

$g(f(x))=(4x+3)-2\\ g(f(x))=4x+3-2\\ g(f(x))=4x+1$

learn more on composite functions here: brainly.com/question/10687170

Answer 2

Answer:

1. 15, 2. -23, 3. 220, 4. 4x-5

Step-by-step explanation:

f(x) = 4x + 3     g(x) = x - 2

1. f(g(5)): Put 5 in as x in g(x)  5 - 2 = 3.  Now put the 3 as x into f(x) and solve. 4(3) + 3 = 15

2. g(f(-6))  4(-6) + 3 = -21. -21 - 2 = -23

3. (f(f(7)) 4(7) + 3 = 31, 31(7) + 3 = 220

4. g(f(x))  4(x-2) + 3  =  4x - 8 + 3  = 4x - 5