Let's evaluate the given function [tex]\( f(x) = 2x^2 - 3 \)[/tex] at the specified values of [tex]\( x \)[/tex].
a. Evaluate [tex]\( f(4) \)[/tex]:
1. Substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[
f(4) = 2(4)^2 - 3
\][/tex]
2. Calculate the square of 4:
[tex]\[
4^2 = 16
\][/tex]
3. Multiply the result by 2:
[tex]\[
2 \cdot 16 = 32
\][/tex]
4. Subtract 3 from the product:
[tex]\[
32 - 3 = 29
\][/tex]
Thus, [tex]\( f(4) = 29 \)[/tex].
b. Evaluate [tex]\( f(-5) \)[/tex]:
1. Substitute [tex]\( x = -5 \)[/tex] into the function:
[tex]\[
f(-5) = 2(-5)^2 - 3
\][/tex]
2. Calculate the square of -5:
[tex]\[
(-5)^2 = 25
\][/tex]
3. Multiply the result by 2:
[tex]\[
2 \cdot 25 = 50
\][/tex]
4. Subtract 3 from the product:
[tex]\[
50 - 3 = 47
\][/tex]
Thus, [tex]\( f(-5) = 47 \)[/tex].
Therefore, the evaluations are:
[tex]\[
a. \quad f(4) = 29
\][/tex]
[tex]\[
b. \quad f(-5) = 47
\][/tex]
