Question

d) if $f(x) = -13 + 7x$ ; find the following.

1. $2f(8) + 7f(2)$ = __________
2. $\frac{f(13)}{4f(3)}$ = __________
3. $-3f(1) \times f(-2)$ = __________
4. $-4f(9) - 6f(0)$ = __________

Explanation:

1) Solve \( 2f(8)+7f(2) \)

Step 1: Find \( f(8) \)

Substitute \( x = 8 \) into \( f(x)=-13 + 7x \).
\( f(8)=-13 + 7\times8=-13 + 56 = 43 \)

Step 2: Find \( f(2) \)

Substitute \( x = 2 \) into \( f(x)=-13 + 7x \).
\( f(2)=-13 + 7\times2=-13 + 14 = 1 \)

Step 3: Calculate \( 2f(8)+7f(2) \)

Substitute \( f(8) = 43 \) and \( f(2)=1 \) into the expression.
\( 2\times43+7\times1 = 86 + 7=93 \)

2) Solve \( \frac{f(13)}{4f(3)} \)

Step 1: Find \( f(13) \)

Substitute \( x = 13 \) into \( f(x)=-13 + 7x \).
\( f(13)=-13 + 7\times13=-13 + 91 = 78 \)

Step 2: Find \( f(3) \)

Substitute \( x = 3 \) into \( f(x)=-13 + 7x \).
\( f(3)=-13 + 7\times3=-13 + 21 = 8 \)

Step 3: Calculate \( \frac{f(13)}{4f(3)} \)

Substitute \( f(13) = 78 \) and \( f(3)=8 \) into the expression.
\( \frac{78}{4\times8}=\frac{78}{32}=\frac{39}{16}=2.4375 \)

3) Solve \( -3f(1)\times f(-2) \)

Step 1: Find \( f(1) \)

Substitute \( x = 1 \) into \( f(x)=-13 + 7x \).
\( f(1)=-13 + 7\times1=-13 + 7=-6 \)

Step 2: Find \( f(-2) \)

Substitute \( x=-2 \) into \( f(x)=-13 + 7x \).
\( f(-2)=-13 + 7\times(-2)=-13-14=-27 \)

Step 3: Calculate \( -3f(1)\times f(-2) \)

Substitute \( f(1)=-6 \) and \( f(-2)=-27 \) into the expression.
\( -3\times(-6)\times(-27)=18\times(-27)=-486 \)

4) Solve \( -4f(9)-6f(0) \)

Step 1: Find \( f(9) \)

Substitute \( x = 9 \) into \( f(x)=-13 + 7x \).
\( f(9)=-13 + 7\times9=-13 + 63 = 50 \)

Step 2: Find \( f(0) \)

Substitute \( x = 0 \) into \( f(x)=-13 + 7x \).
\( f(0)=-13 + 7\times0=-13 \)

Step 3: Calculate \( -4f(9)-6f(0) \)

Substitute \( f(9) = 50 \) and \( f(0)=-13 \) into the expression.
\( -4\times50-6\times(-13)=-200 + 78=-122 \)

Answer:

s:

1. \( \boldsymbol{93} \)
2. \( \boldsymbol{\frac{39}{16}} \) (or \( 2.4375 \))
3. \( \boldsymbol{-486} \)
4. \( \boldsymbol{-122} \)