Certainly! Let's evaluate the given functions [tex]\( f(x) \)[/tex], [tex]\( g(x) \)[/tex], and [tex]\( h(x) \)[/tex] at [tex]\( x = 1 \)[/tex] in a detailed, step-by-step manner.
### Step-by-Step Solution
1. Evaluating [tex]\( f(x) \)[/tex]:
Given the function:
[tex]\[
f(x) = 9x - 5
\][/tex]
We need to find [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 9(1) - 5
\][/tex]
Calculating inside the parentheses:
[tex]\[
9 \times 1 = 9
\][/tex]
Subtracting 5:
[tex]\[
9 - 5 = 4
\][/tex]
Thus:
[tex]\[
f(1) = 4
\][/tex]
2. Evaluating [tex]\( g(x) \)[/tex]:
Given the function:
[tex]\[
g(x) = 4x^2 + 12
\][/tex]
We need to find [tex]\( g(1) \)[/tex]:
[tex]\[
g(1) = 4(1)^2 + 12
\][/tex]
Evaluating the square of [tex]\( 1 \)[/tex]:
[tex]\[
1^2 = 1
\][/tex]
Multiplying by 4:
[tex]\[
4 \times 1 = 4
\][/tex]
Adding 12:
[tex]\[
4 + 12 = 16
\][/tex]
Thus:
[tex]\[
g(1) = 16
\][/tex]
3. Evaluating [tex]\( h(x) \)[/tex]:
Given the function:
[tex]\[
h(x) = x^2 + 20x - 40
\][/tex]
We need to find [tex]\( h(1) \)[/tex]:
[tex]\[
h(1) = (1)^2 + 20(1) - 40
\][/tex]
Evaluating the square of [tex]\( 1 \)[/tex]:
[tex]\[
1^2 = 1
\][/tex]
Multiplying [tex]\( 20 \)[/tex] by [tex]\( 1 \)[/tex]:
[tex]\[
20 \times 1 = 20
\][/tex]
Summing these values and subtracting 40:
[tex]\[
1 + 20 - 40 = 21 - 40 = -19
\][/tex]
Thus:
[tex]\[
h(1) = -19
\][/tex]
### Summary:
- [tex]\( f(1) = 4 \)[/tex]
- [tex]\( g(1) = 16 \)[/tex]
- [tex]\( h(1) = -19 \)[/tex]
So the results of evaluating the functions [tex]\( f(x) \)[/tex], [tex]\( g(x) \)[/tex], and [tex]\( h(x) \)[/tex] at [tex]\( x = 1 \)[/tex] are [tex]\( 4 \)[/tex], [tex]\( 16 \)[/tex], and [tex]\( -19 \)[/tex] respectively.
