Absolutely! Let's go through the detailed step-by-step solutions for each requested value of the function [tex]\( f(x) = 3x^2 - 5x \)[/tex].
### Part a) [tex]\( f(2) \)[/tex]
For [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 3(2)^2 - 5(2)
\][/tex]
This evaluates to:
[tex]\[
f(2) = 3 \cdot 4 - 5 \cdot 2 = 12 - 10 = 2
\][/tex]
Thus:
[tex]\[
f(2) = 2
\][/tex]
### Part b) [tex]\( f(-8) \)[/tex]
For [tex]\( x = -8 \)[/tex]:
[tex]\[
f(-8) = 3(-8)^2 - 5(-8)
\][/tex]
This evaluates to:
[tex]\[
f(-8) = 3 \cdot 64 - 5 \cdot (-8) = 192 + 40 = 232
\][/tex]
Thus:
[tex]\[
f(-8) = 232
\][/tex]
### Part c) [tex]\( f(7) \)[/tex]
For [tex]\( x = 7 \)[/tex]:
[tex]\[
f(7) = 3(7)^2 - 5(7)
\][/tex]
This evaluates to:
[tex]\[
f(7) = 3 \cdot 49 - 5 \cdot 7 = 147 - 35 = 112
\][/tex]
Thus:
[tex]\[
f(7) = 112
\][/tex]
### Part d) [tex]\( f(-1) \)[/tex]
For [tex]\( x = -1 \)[/tex]:
[tex]\[
f(-1) = 3(-1)^2 - 5(-1)
\][/tex]
This evaluates to:
[tex]\[
f(-1) = 3 \cdot 1 - 5 \cdot (-1) = 3 + 5 = 8
\][/tex]
Thus:
[tex]\[
f(-1) = 8
\][/tex]
In summary:
[tex]\[
f(2) = 2, \quad f(-8) = 232, \quad f(7) = 112, \quad f(-1) = 8
\][/tex]
