Answer :
Sure! To find the value of [tex]\( f(-6) \)[/tex] given the function [tex]\( f(x) = 4(3 - x) + 10 \)[/tex], we will substitute [tex]\(-6\)[/tex] into the function and simplify.
1. Start with the function:
[tex]\[ f(x) = 4(3 - x) + 10 \][/tex]
2. Substitute [tex]\(-6\)[/tex] for [tex]\(x\)[/tex]:
[tex]\[ f(-6) = 4(3 - (-6)) + 10 \][/tex]
3. Simplify inside the parentheses:
[tex]\[ 3 - (-6) = 3 + 6 = 9 \][/tex]
4. Now, the expression is:
[tex]\[ f(-6) = 4 \cdot 9 + 10 \][/tex]
5. Multiply [tex]\(4 \cdot 9\)[/tex]:
[tex]\[ 4 \cdot 9 = 36 \][/tex]
6. Finally, add [tex]\(10\)[/tex] to [tex]\(36\)[/tex]:
[tex]\[ 36 + 10 = 46 \][/tex]
So, the value of [tex]\( f(-6) \)[/tex] is [tex]\( 46 \)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{46}
\][/tex]
1. Start with the function:
[tex]\[ f(x) = 4(3 - x) + 10 \][/tex]
2. Substitute [tex]\(-6\)[/tex] for [tex]\(x\)[/tex]:
[tex]\[ f(-6) = 4(3 - (-6)) + 10 \][/tex]
3. Simplify inside the parentheses:
[tex]\[ 3 - (-6) = 3 + 6 = 9 \][/tex]
4. Now, the expression is:
[tex]\[ f(-6) = 4 \cdot 9 + 10 \][/tex]
5. Multiply [tex]\(4 \cdot 9\)[/tex]:
[tex]\[ 4 \cdot 9 = 36 \][/tex]
6. Finally, add [tex]\(10\)[/tex] to [tex]\(36\)[/tex]:
[tex]\[ 36 + 10 = 46 \][/tex]
So, the value of [tex]\( f(-6) \)[/tex] is [tex]\( 46 \)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{46}
\][/tex]