Question

Evaluate the following functions
A. W(n)=4n+2, find w(3n)
B. H(x)=4x_2, find h(x+2)
C. G(n)=n³_5n², find g(_4n)
D. P(a)=a³_5, find p(x_4)

Answer 1

Let's evaluate each of the functions step-by-step.

### A. \( W(n) = 4n + 2 \), find \( W(3n) \)

To find \( W(3n) \):
\[
W(3n) = 4(3n) + 2
\]
\[
= 12n + 2
\]

### B. \( H(x) = 4x^2 \), find \( H(x + 2) \)

To find \( H(x + 2) \):
\[
H(x + 2) = 4(x + 2)^2
\]
Expanding \( (x + 2)^2 \):
\[
= 4(x^2 + 4x + 4)
\]
\[
= 4x^2 + 16x + 16
\]

### C. \( G(n) = n^3 - 5n^2 \), find \( G(4n) \)

To find \( G(4n) \):
\[
G(4n) = (4n)^3 - 5(4n)^2
\]
Calculating \( (4n)^3 \) and \( (4n)^2 \):
\[
= 64n^3 - 5(16n^2)
\]
\[
= 64n^3 - 80n^2
\]

### D. \( P(a) = a^3 - 5 \), find \( P(x + 4) \)

To find \( P(x + 4) \):
\[
P(x + 4) = (x + 4)^3 - 5
\]
Expanding \( (x + 4)^3 \):
\[
(x + 4)^3 = x^3 + 3(x^2)(4) + 3(x)(4^2) + 4^3
\]
\[
= x^3 + 12x^2 + 48x + 64
\]
Thus,
\[
P(x + 4) = (x^3 + 12x^2 + 48x + 64) - 5
\]
\[
= x^3 + 12x^2 + 48x + 59
\]

### Summary of Results:

A. \( W(3n) = 12n + 2 \)

B. \( H(x + 2) = 4x^2 + 16x + 16 \)

C. \( G(4n) = 64n^3 - 80n^2 \)

D. \( P(x + 4) = x^3 + 12x^2 + 48x + 59 \)