To find the value of [tex]\( 2 f(x) - 3 \)[/tex] given the function [tex]\( f(x) = 2x^2 + 7 \)[/tex], let's follow the steps carefully:
1. Define the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(x) = 2x^2 + 7
\][/tex]
2. Evaluate [tex]\( f(0) \)[/tex]:
[tex]\[
f(0) = 2(0)^2 + 7 = 0 + 7 = 7
\][/tex]
3. Find the expression [tex]\( 2 f(x) - 3 \)[/tex]:
[tex]\[
2 f(x) - 3 = 2 (2x^2 + 7) - 3
\][/tex]
4. Simplify the expression inside the parentheses:
[tex]\[
2 (2x^2 + 7) = 2 \cdot 2x^2 + 2 \cdot 7 = 4x^2 + 14
\][/tex]
5. Combine like terms:
[tex]\[
2 f(x) - 3 = 4x^2 + 14 - 3 = 4x^2 + 11
\][/tex]
6. To find the specific value at [tex]\( x = 0 \)[/tex], substitute [tex]\( x = 0 \)[/tex] into the simplified expression:
[tex]\[
4 (0)^2 + 11 = 0 + 11 = 11
\][/tex]
Therefore, the value of [tex]\( 2 f(x) - 3 \)[/tex] when [tex]\( x = 0 \)[/tex] is [tex]\( 11 \)[/tex].
To summarize:
- [tex]\( f(0) \)[/tex] is [tex]\( 7 \)[/tex]
- [tex]\( 2 f(0) - 3 \)[/tex] is [tex]\( 11 \)[/tex]
So, the final answer is:
[tex]\[
2 f(0) - 3 = 11
\][/tex]
