Let's break down the solution to each part of the problem step-by-step:
### Part 1: Calculation of [tex]\( f(4) \)[/tex]
We are given the function [tex]\( f(x) = 3x - 5 \)[/tex].
To find [tex]\( f(4) \)[/tex]:
1. Substitute [tex]\( 4 \)[/tex] into the function:
[tex]\[
f(4) = 3(4) - 5
\][/tex]
2. Simplify the expression:
[tex]\[
f(4) = 12 - 5 = 7
\][/tex]
So, [tex]\( f(4) = 7 \)[/tex].
This result indicates that the value of the function at [tex]\( x=4 \)[/tex] is [tex]\( 7 \)[/tex], which can be represented as the ordered pair [tex]\( (4, 7) \)[/tex].
### Part 2: Calculation of [tex]\( h(-3) \)[/tex]
We are given the function [tex]\( h(h) = 3h^2 - 2h + 1 \)[/tex].
To find [tex]\( h(-3) \)[/tex]:
1. Substitute [tex]\( -3 \)[/tex] into the function:
[tex]\[
h(-3) = 3(-3)^2 - 2(-3) + 1
\][/tex]
2. Simplify the expression step-by-step:
[tex]\[
h(-3) = 3(9) + 6 + 1
\][/tex]
[tex]\[
h(-3) = 27 + 6 + 1 = 34
\][/tex]
So, [tex]\( h(-3) = 34 \)[/tex].
This result indicates that the value of the function at [tex]\( h = -3 \)[/tex] is [tex]\( 34 \)[/tex].
### Part 3: Calculation of [tex]\( g(2) \)[/tex]
We are given the function [tex]\( g(x) = x^2 - 2x + 1 \)[/tex].
To find [tex]\( g(2) \)[/tex]:
1. Substitute [tex]\( 2 \)[/tex] into the function:
[tex]\[
g(2) = 2^2 - 2(2) + 1
\][/tex]
2. Simplify the expression step-by-step:
[tex]\[
g(2) = 4 - 4 + 1 = 1
\][/tex]
So, [tex]\( g(2) = 1 \)[/tex].
This result indicates that the value of the function at [tex]\( x=2 \)[/tex] is [tex]\( 1 \)[/tex].
### Summary
The results for each part are:
1. [tex]\( f(4) = 7 \)[/tex]
2. [tex]\( h(-3) = 34 \)[/tex]
3. [tex]\( g(2) = 1 \)[/tex]
These calculations show the specific values for the given functions at the provided inputs.
