Certainly! Let's break down the problem step-by-step.
We're given two functions:
[tex]\( f(x) = 2x^2 + 3 \)[/tex]
[tex]\( g(x) = x^2 - 7 \)[/tex]
To find the value of these functions at a specific point, we need to choose a value for [tex]\( x \)[/tex]. Let's use [tex]\( x = 1 \)[/tex].
### Let's evaluate [tex]\( f(x) \)[/tex] for [tex]\( x = 1 \)[/tex]:
1. Start by substituting [tex]\( x = 1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(1) = 2(1)^2 + 3
\][/tex]
2. Calculate the square of 1:
[tex]\[
1^2 = 1
\][/tex]
3. Multiply the result by 2:
[tex]\[
2 \times 1 = 2
\][/tex]
4. Add 3 to the result:
[tex]\[
2 + 3 = 5
\][/tex]
So, [tex]\( f(1) = 5 \)[/tex].
### Now, let's evaluate [tex]\( g(x) \)[/tex] for [tex]\( x = 1 \)[/tex]:
1. Substitute [tex]\( x = 1 \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(1) = (1)^2 - 7
\][/tex]
2. Calculate the square of 1:
[tex]\[
1^2 = 1
\][/tex]
3. Subtract 7 from the result:
[tex]\[
1 - 7 = -6
\][/tex]
So, [tex]\( g(1) = -6 \)[/tex].
### Final Answer:
For [tex]\( x = 1 \)[/tex]:
- [tex]\( f(1) = 5 \)[/tex]
- [tex]\( g(1) = -6 \)[/tex]
So the results are [tex]\( (5, -6) \)[/tex].
