Let fx1x4 and gx2x4 Find the following functions Simplify yo

Let f(x)=1x4 and g(x)=2x+4.

Find the following functions. Simplify your answers.

f(g(x))=     ,

g(f(x))=     .

The function h(x)=(x+1)4 can be expressed in the form f(g(x)) where f(x)=x4, and g(x) is defined below:

g(x)=     ,

he function h(x)=1x+4 can be expressed in the form f(g(x)) where g(x)=(x+4) and f(x) is defined as:

f(x)

The function D(p) gives the number of items that will be demanded when the price is p. The production cost, C(x) is the cost of producing x items. To determine the cost of production when the price is $6, you would:

Evaluate C(D(6))

Solve C(D(p))=6

Evaluate D(C(6))

Solve D(C(x))=6

Given the following functions, find each of the values:

f(x)=x2x42

g(x)=x+6

(f+g)(3)=

(fg)(4)=

(fg)(2)=

(fg)(3)

Given the following functions, find each:

f(x)=x2+8x+7

g(x)=x+7

(f+g)(x)=    

(fg)(x)=    

(fg)(x)=    

Solution

1) f(x) = x4 and g(x) = 2x+4

f(g(x)) = f(2x+4)

==> f(2x+4) = 2x+4 -4 = 2x

g(f(x)) = g(x -4)

==> g(x -4) = 2(x -4)+4 = 2x -4

2) h(x) = (x +1)⁴ , f(x) = x⁴

h(x) = f(g(x)) = (x +1)⁴

==> g(x) = x +1

3) h(x) = x +4 , g(x) = x +4

h(x) = f(g(x))

= f(x +4) = x +4

==> f(x) = x