Answer :
To find the value of [tex]\( f(3, 2) \)[/tex] for the function [tex]\( f(x, y) = 3x^2 - 4y \)[/tex], we can follow these steps:
1. Identify the function: The function is given as [tex]\( f(x, y) = 3x^2 - 4y \)[/tex]. It involves two variables, [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
2. Plug in the values: We need to calculate [tex]\( f(3, 2) \)[/tex]. This means plugging [tex]\( x = 3 \)[/tex] and [tex]\( y = 2 \)[/tex] into the function.
3. Calculate [tex]\( x^2 \)[/tex]: First, we compute [tex]\( x^2 \)[/tex] where [tex]\( x = 3 \)[/tex].
[tex]\[
3^2 = 9
\][/tex]
4. Multiply by the coefficient: Multiply the result by 3.
[tex]\[
3 \times 9 = 27
\][/tex]
5. Calculate the [tex]\( y \)[/tex] term: Multiply 4 by [tex]\( y = 2 \)[/tex].
[tex]\[
4 \times 2 = 8
\][/tex]
6. Subtract the [tex]\( y \)[/tex] term from the [tex]\( x \)[/tex] term: Subtract the result of the [tex]\( y \)[/tex] term from the result of the [tex]\( x \)[/tex] term.
[tex]\[
27 - 8 = 19
\][/tex]
Therefore, the value of [tex]\( f(3, 2) \)[/tex] is [tex]\(\boxed{19}\)[/tex].
1. Identify the function: The function is given as [tex]\( f(x, y) = 3x^2 - 4y \)[/tex]. It involves two variables, [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
2. Plug in the values: We need to calculate [tex]\( f(3, 2) \)[/tex]. This means plugging [tex]\( x = 3 \)[/tex] and [tex]\( y = 2 \)[/tex] into the function.
3. Calculate [tex]\( x^2 \)[/tex]: First, we compute [tex]\( x^2 \)[/tex] where [tex]\( x = 3 \)[/tex].
[tex]\[
3^2 = 9
\][/tex]
4. Multiply by the coefficient: Multiply the result by 3.
[tex]\[
3 \times 9 = 27
\][/tex]
5. Calculate the [tex]\( y \)[/tex] term: Multiply 4 by [tex]\( y = 2 \)[/tex].
[tex]\[
4 \times 2 = 8
\][/tex]
6. Subtract the [tex]\( y \)[/tex] term from the [tex]\( x \)[/tex] term: Subtract the result of the [tex]\( y \)[/tex] term from the result of the [tex]\( x \)[/tex] term.
[tex]\[
27 - 8 = 19
\][/tex]
Therefore, the value of [tex]\( f(3, 2) \)[/tex] is [tex]\(\boxed{19}\)[/tex].
