### Given:
Functions:
[tex]\[ p(x) = 2 \times 7 + 5x - 3 \][/tex]
[tex]\[ m(x) = 2x - 1 \][/tex]
[tex]\[ h(x) = 2x + 1 \][/tex]
We need to find the following:
### 1. [tex]\((m - p)(x)\)[/tex]
First, let's express [tex]\((m - p)(x)\)[/tex]:
[tex]\[ m(x) - p(x) = (2x - 1) - (2 \times 7 + 5x - 3) \][/tex]
[tex]\[ = 2x - 1 - 14 - 5x + 3 \][/tex]
[tex]\[ = 2x - 5x - 1 + 3 - 14 \][/tex]
[tex]\[ = -3x + 2 - 14 \][/tex]
[tex]\[ = -3x - 12 \][/tex]
Next, compute this for [tex]\(x = 1\)[/tex]:
[tex]\[ (m - p)(1) = -3(1) - 12 \][/tex]
[tex]\[ = -3 - 12 \][/tex]
[tex]\[ = -15 \][/tex]
So, [tex]\((m - p)(1) = -15\)[/tex].
### 2. [tex]\(p(5) + m(3) - h(1)\)[/tex]
Calculate each value step-by-step:
[tex]\[ p(5) = 2 \times 7 + 5 \times 5 - 3 \][/tex]
[tex]\[ = 14 + 25 - 3 \][/tex]
[tex]\[ = 36 \][/tex]
[tex]\[ m(3) = 2 \times 3 - 1 \][/tex]
[tex]\[ = 6 - 1 \][/tex]
[tex]\[ = 5 \][/tex]
[tex]\[ h(1) = 2 \times 1 + 1 \][/tex]
[tex]\[ = 2 + 1 \][/tex]
[tex]\[ = 3 \][/tex]
Now, sum these results:
[tex]\[ p(5) + m(3) - h(1) = 36 + 5 - 3 \][/tex]
[tex]\[ = 38 \][/tex]
### 3. [tex]\( m(x) \)[/tex]
Given:
[tex]\[ m(x) = 2x - 1 \][/tex]
So, the result for [tex]\( m(x) \)[/tex] remains [tex]\[ m(x) = 2x - 1 \][/tex].
### 4. [tex]\( p(x+1) \)[/tex]
Substitute [tex]\( x+1 \)[/tex] into [tex]\( p(x) \)[/tex]:
[tex]\[ p(x+1) = 2 \times 7 + 5(x+1) - 3 \][/tex]
[tex]\[ = 14 + 5x + 5 - 3 \][/tex]
[tex]\[ = 14 + 5x + 2 \][/tex]
[tex]\[ = 16 + 5x \][/tex]
Now, compute this for [tex]\( x = 2 \)[/tex]:
[tex]\[ p(2 + 1) = 16 + 5 \times 2 \][/tex]
[tex]\[ = 16 + 10 \][/tex]
[tex]\[ = 26 \][/tex]
### 5. [tex]\( p(3) - 3(m(2)) \)[/tex]
First, compute [tex]\( p(3) \)[/tex]:
[tex]\[ p(3) = 2 \times 7 + 5 \times 3 - 3 \][/tex]
[tex]\[ = 14 + 15 - 3 \][/tex]
[tex]\[ = 26 \][/tex]
Next, compute [tex]\( m(2) \)[/tex]:
[tex]\[ m(2) = 2 \times 2 - 1 \][/tex]
[tex]\[ = 4 - 1 \][/tex]
[tex]\[ = 3 \][/tex]
Now, compute [tex]\( 3(m(2)) \)[/tex]:
[tex]\[ 3(m(2)) = 3 \times 3 \][/tex]
[tex]\[ = 9 \][/tex]
Finally:
[tex]\[ p(3) - 3(m(2)) = 26 - 9 \][/tex]
[tex]\[ = 17 \][/tex]
### Summary:
1. [tex]\((m - p)(1) = -15\)[/tex]
2. [tex]\(p(5) + m(3) - h(1) = 38\)[/tex]
3. [tex]\(m(x) = 2x - 1\)[/tex]
4. [tex]\(p(x+1) = 16 + 5x\)[/tex] and [tex]\(p(2 + 1) = 26\)[/tex]
5. [tex]\(p(3) - 3(m(2)) = 17\)[/tex]
