To compute [tex]\( f(3) \)[/tex] for the given function [tex]\( f(x) = 7x^2 + 5 \)[/tex], follow these steps:
1. Identify the given function and the value of [tex]\( x \)[/tex]:
- The function is [tex]\( f(x) = 7x^2 + 5 \)[/tex].
- We need to find the value of the function when [tex]\( x = 3 \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
- Replace [tex]\( x \)[/tex] with 3 in the function.
3. Simplify the expression:
- First, calculate the square of 3.
- Multiply the result by 7.
- Finally, add 5 to the product obtained.
Following these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\( f(3) = 7(3)^2 + 5 \)[/tex].
2. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\( 3^2 = 9 \)[/tex].
3. Multiply 7 by 9:
[tex]\( 7 \times 9 = 63 \)[/tex].
4. Add 5 to the product:
[tex]\( 63 + 5 = 68 \)[/tex].
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 68 \)[/tex].
