Find (fg)(x) for: f(x) = (x - 4)2 (x + 2x) ; g(x) = (2x) (x - 4) a) (x - 4) 3 b) (x + 4) 3 c) 2(x - 4) 3 d) 2(x + 4) 3

Set up the composite result function.

f

(

g

(

x

)

)

Evaluate  

f

(

g

(

x

)

)

by substituting in the value of  

g

into  

f

.

3

(

2

x

+

1

)

−

5

Simplify each term.

f

(

2

x

+

1

)

=

6

x

+

3

−

5

Subtract  

5

from  

3

.

f

(

2

x

+

1

)

=

6

x

−

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions