Answer :
Let's find the value of [tex]\( f(5) \)[/tex] for the given function [tex]\( f(x) = 3x^2 + 2x - 1 \)[/tex].
1. Start by substituting [tex]\( x \)[/tex] with 5 in the function:
[tex]\[ f(x) = 3x^2 + 2x - 1 \][/tex]
2. Plug [tex]\( x = 5 \)[/tex] into the function:
[tex]\[ f(5) = 3(5)^2 + 2(5) - 1 \][/tex]
3. Calculate [tex]\( (5)^2 \)[/tex]:
[tex]\[ 5^2 = 25 \][/tex]
4. Multiply 25 by 3:
[tex]\[ 3 \cdot 25 = 75 \][/tex]
5. Multiply 2 by 5:
[tex]\[ 2 \cdot 5 = 10 \][/tex]
6. Add these results together:
[tex]\[ 75 + 10 = 85 \][/tex]
7. Finally, subtract 1:
[tex]\[ 85 - 1 = 84 \][/tex]
So, the value of [tex]\( f(5) \)[/tex] is [tex]\( 84 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{84} \][/tex]
1. Start by substituting [tex]\( x \)[/tex] with 5 in the function:
[tex]\[ f(x) = 3x^2 + 2x - 1 \][/tex]
2. Plug [tex]\( x = 5 \)[/tex] into the function:
[tex]\[ f(5) = 3(5)^2 + 2(5) - 1 \][/tex]
3. Calculate [tex]\( (5)^2 \)[/tex]:
[tex]\[ 5^2 = 25 \][/tex]
4. Multiply 25 by 3:
[tex]\[ 3 \cdot 25 = 75 \][/tex]
5. Multiply 2 by 5:
[tex]\[ 2 \cdot 5 = 10 \][/tex]
6. Add these results together:
[tex]\[ 75 + 10 = 85 \][/tex]
7. Finally, subtract 1:
[tex]\[ 85 - 1 = 84 \][/tex]
So, the value of [tex]\( f(5) \)[/tex] is [tex]\( 84 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{84} \][/tex]
