for the function f defined by:
(x)=3x^2+3x+2;find the following values.
a. f(-1)=
b. f(-x)=
c. -f(x)=
d. f(x+h)=
f(-1) = 2
f(-x) = 3x^2 - 3x + 2
-f(x) = -3x^2 - 3x - 2
f(x+h) = 3(x+h)^2 + 3(x+h) + 2
Thank you so much for the help. I was off course.
To find the values of the function f for different inputs, we can simply substitute the inputs into the given function and perform the necessary calculations as follows:
a. To find f(-1), we substitute -1 into the function:
f(-1) = 3(-1)^2 + 3(-1) + 2
= 3(1) - 3 + 2
= 3 - 3 + 2
= 2
Therefore, f(-1) equals 2.
b. To find f(-x), we substitute -x into the function:
f(-x) = 3(-x)^2 + 3(-x) + 2
= 3x^2 - 3x + 2
Therefore, f(-x) equals 3x^2 - 3x + 2.
c. To find -f(x), we substitute x into the function and multiply it by -1:
-f(x) = -1 * (3x^2 + 3x + 2)
= -3x^2 - 3x - 2
Therefore, -f(x) equals -3x^2 - 3x - 2.
d. To find f(x+h), we substitute x + h into the function:
f(x+h) = 3(x+h)^2 + 3(x+h) + 2
= 3(x^2 + 2xh + h^2) + 3x + 3h + 2
= 3x^2 + 6xh + 3h^2 + 3x + 3h + 2
Therefore, f(x+h) equals 3x^2 + 6xh + 3h^2 + 3x + 3h + 2.
By performing the appropriate substitutions, we have found the values for each of the given expressions.