Answer :
Let's solve this problem step-by-step:
We need to find the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 12 \)[/tex]. The function is given by:
[tex]\[ f(x) = \frac{2}{3}x + 9x \][/tex]
First, let's combine the terms:
1. Notice that [tex]\(\frac{2}{3}x + 9x\)[/tex] can be rewritten by factoring out [tex]\(x\)[/tex]:
[tex]\[ f(x) = \left( \frac{2}{3} + 9 \right)x \][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[ \frac{2}{3} + 9 = \frac{2}{3} + \frac{27}{3} = \frac{2 + 27}{3} = \frac{29}{3} \][/tex]
So, the function simplifies to:
[tex]\[ f(x) = \frac{29}{3}x \][/tex]
Now, substitute [tex]\( x = 12 \)[/tex] into this simplified expression:
[tex]\[ f(12) = \frac{29}{3} \times 12 \][/tex]
Calculate this product:
[tex]\[ f(12) = \frac{29 \times 12}{3} \][/tex]
[tex]\[ f(12) = \frac{348}{3} \][/tex]
[tex]\[ f(12) = 116 \][/tex]
Therefore, the value of [tex]\( f(12) \)[/tex] is 116, which corresponds to option (a).
We need to find the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 12 \)[/tex]. The function is given by:
[tex]\[ f(x) = \frac{2}{3}x + 9x \][/tex]
First, let's combine the terms:
1. Notice that [tex]\(\frac{2}{3}x + 9x\)[/tex] can be rewritten by factoring out [tex]\(x\)[/tex]:
[tex]\[ f(x) = \left( \frac{2}{3} + 9 \right)x \][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[ \frac{2}{3} + 9 = \frac{2}{3} + \frac{27}{3} = \frac{2 + 27}{3} = \frac{29}{3} \][/tex]
So, the function simplifies to:
[tex]\[ f(x) = \frac{29}{3}x \][/tex]
Now, substitute [tex]\( x = 12 \)[/tex] into this simplified expression:
[tex]\[ f(12) = \frac{29}{3} \times 12 \][/tex]
Calculate this product:
[tex]\[ f(12) = \frac{29 \times 12}{3} \][/tex]
[tex]\[ f(12) = \frac{348}{3} \][/tex]
[tex]\[ f(12) = 116 \][/tex]
Therefore, the value of [tex]\( f(12) \)[/tex] is 116, which corresponds to option (a).
