Worksheet for practicing function operations with algebraic expressions.

To solve the given function operations, we will evaluate each problem step by step. Here are the solutions:

---

Problem 1:

Given:
- \( g(k) = k^2 - 3k + 11 \)
- Find \( g(8) \)

#### Solution:
Substitute \( k = 8 \) into \( g(k) \):
\[
g(8) = 8^2 - 3(8) + 11
\]
\[
g(8) = 64 - 24 + 11
\]
\[
g(8) = 51
\]

Answer:
\[
\boxed{51}
\]

---

Problem 2:

Given:
- \( p(m) = m + 9 \)
- \( q(m) = m - 10 \)
- Find \( p(3) \) and \( q(3) \)

#### Solution:
1. Evaluate \( p(3) \):
\[
p(3) = 3 + 9 = 12
\]

2. Evaluate \( q(3) \):
\[
q(3) = 3 - 10 = -7
\]

Answer:
\[
\boxed{12, -7}
\]

---

Problem 3:

Given:
- \( f(x) = x^2 + 7x + 9 \)
- \( g(x) = x^2 + x + 7 \)
- Find \( f(2) \) and \( g(2) \)

#### Solution:
1. Evaluate \( f(2) \):
\[
f(2) = 2^2 + 7(2) + 9
\]
\[
f(2) = 4 + 14 + 9
\]
\[
f(2) = 27
\]

2. Evaluate \( g(2) \):
\[
g(2) = 2^2 + 2 + 7
\]
\[
g(2) = 4 + 2 + 7
\]
\[
g(2) = 13
\]

Answer:
\[
\boxed{27, 13}
\]

---

Problem 4:

Given:
- \( h(x) = 9x - 6 \)
- \( l(x) = 10x - 3 \)
- Find \( h(1) \) and \( l(1) \)

#### Solution:
1. Evaluate \( h(1) \):
\[
h(1) = 9(1) - 6
\]
\[
h(1) = 9 - 6
\]
\[
h(1) = 3
\]

2. Evaluate \( l(1) \):
\[
l(1) = 10(1) - 3
\]
\[
l(1) = 10 - 3
\]
\[
l(1) = 7
\]

Answer:
\[
\boxed{3, 7}
\]

---

Problem 5:

Given:
- \( f(x) = x^2 + 6 \)
- \( g(x) = x^2 + 2x \)
- Find \( f(0) \) and \( g(0) \)

#### Solution:
1. Evaluate \( f(0) \):
\[
f(0) = 0^2 + 6
\]
\[
f(0) = 6
\]

2. Evaluate \( g(0) \):
\[
g(0) = 0^2 + 2(0)
\]
\[
g(0) = 0
\]

Answer:
\[
\boxed{6, 0}
\]

---

Problem 6:

Given:
- \( h(x) = x^2 + 2x - 9 \)
- \( g(x) = x^2 + 10x - 11 \)
- Find \( h(2) \) and \( g(7) \)

#### Solution:
1. Evaluate \( h(2) \):
\[
h(2) = 2^2 + 2(2) - 9
\]
\[
h(2) = 4 + 4 - 9
\]
\[
h(2) = -1
\]

2. Evaluate \( g(7) \):
\[
g(7) = 7^2 + 10(7) - 11
\]
\[
g(7) = 49 + 70 - 11
\]
\[
g(7) = 108
\]

Answer:
\[
\boxed{-1, 108}
\]

---

Problem 7:

Given:
- \( g(n) = n^2 - 6n - 4 \)
- \( l(n) = 7n + 10 \)
- Find \( g(1) \) and \( l(1) \)

#### Solution:
1. Evaluate \( g(1) \):
\[
g(1) = 1^2 - 6(1) - 4
\]
\[
g(1) = 1 - 6 - 4
\]
\[
g(1) = -9
\]

2. Evaluate \( l(1) \):
\[
l(1) = 7(1) + 10
\]
\[
l(1) = 7 + 10
\]
\[
l(1) = 17
\]

Answer:
\[
\boxed{-9, 17}
\]

---

Problem 8:

Given:
- \( g(k) = k^2 + 11k + 8 \)
- \( l(k) = 7k + 8 \)
- Find \( g(k) \) and \( l(k) \)

#### Solution:
This problem seems to be incomplete because it does not specify a value for \( k \). If you meant to find \( g(k) \) and \( l(k) \) in general, they are already given as:
\[
g(k) = k^2 + 11k + 8
\]
\[
l(k) = 7k + 8
\]

If you intended to evaluate at a specific \( k \), please clarify.

---

Problem 9:

Given:
- \( g(k) = k^2 + 2k + 9 \)
- \( l(k) = 2k + 11 \)
- Find \( g(k) \) and \( l(k) \)

#### Solution:
Similar to Problem 8, this problem is incomplete without specifying a value for \( k \). The functions are:
\[
g(k) = k^2 + 2k + 9
\]
\[
l(k) = 2k + 11
\]

If you intended to evaluate at a specific \( k \), please clarify.

---

Problem 10:

Given:
- \( p(m) = m^2 + 2m \)
- \( t(m) = -m + 3 \)
- Find \( p(9) \) and \( t(9) \)

#### Solution:
1. Evaluate \( p(9) \):
\[
p(9) = 9^2 + 2(9)
\]
\[
p(9) = 81 + 18
\]
\[
p(9) = 99
\]

2. Evaluate \( t(9) \):
\[
t(9) = -9 + 3
\]
\[
t(9) = -6
\]

Answer:
\[
\boxed{99, -6}
\]

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Final Answers:

1. \(\boxed{51}\)
2. \(\boxed{12, -7}\)
3. \(\boxed{27, 13}\)
4. \(\boxed{3, 7}\)
5. \(\boxed{6, 0}\)
6. \(\boxed{-1, 108}\)
7. \(\boxed{-9, 17}\)
8. Incomplete (functions provided: \( g(k) = k^2 + 11k + 8 \), \( l(k) = 7k + 8 \))
9. Incomplete (functions provided: \( g(k) = k^2 + 2k + 9 \), \( l(k) = 2k + 11 \))
10. \(\boxed{99, -6}\)