To solve the given problem, we need to evaluate the expression [tex]\((f+g)(1)\)[/tex]. Here, we have two functions: [tex]\( f(x) = 2x + 210 \)[/tex], which represents the calories burned from exercising for [tex]\( x \)[/tex] hours, and [tex]\( g(x) = 2x + 125 \)[/tex], which represents the calorie deficit from dieting for [tex]\( x \)[/tex] hours.
The notation [tex]\((f + g)(1)\)[/tex] means we need to add the values of [tex]\( f(1) \)[/tex] and [tex]\( g(1) \)[/tex].
Step-by-Step Solution:
1. Evaluate [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 2(1) + 210 = 2 + 210 = 212
\][/tex]
2. Evaluate [tex]\( g(1) \)[/tex]:
[tex]\[
g(1) = 2(1) + 125 = 2 + 125 = 127
\][/tex]
3. Sum the results:
[tex]\[
(f + g)(1) = f(1) + g(1) = 212 + 127 = 339
\][/tex]
Therefore, [tex]\((f + g)(1) = 339\)[/tex].
Now, let's interpret the context of the problem:
- Function [tex]\( f(x) \)[/tex] represents calories burned while exercising, and [tex]\( x \)[/tex] is the number of hours of exercise.
- Function [tex]\( g(x) \)[/tex] represents the calorie deficit from dieting, and [tex]\( x \)[/tex] is also related to the number of hours of exercise.
When we combine the effect for 1 hour, we sum up the calories burned from both exercising and dieting.
Therefore, the correct answer is:
b. 339 calories burned while combining diet with 1 hour of exercise.
