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If f(x)=2x^(2)+4 for all real numbers x,...

If `f(x)=2x^(2)+4` for all real numbers x, which of the following is equal to `f(3)+f(5)`?

A

`f(4)`

B

`f(6)`

C

`f(10)`

D

`f(15)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to find the value of \( f(3) + f(5) \) given that \( f(x) = 2x^2 + 4 \). ### Step-by-Step Solution: 1. **Calculate \( f(3) \)**: \[ f(3) = 2(3^2) + 4 \] \[ = 2(9) + 4 \] \[ = 18 + 4 \] \[ = 22 \] 2. **Calculate \( f(5) \)**: \[ f(5) = 2(5^2) + 4 \] \[ = 2(25) + 4 \] \[ = 50 + 4 \] \[ = 54 \] 3. **Add \( f(3) \) and \( f(5) \)**: \[ f(3) + f(5) = 22 + 54 \] \[ = 76 \] ### Final Answer: Thus, \( f(3) + f(5) = 76 \).
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