The values of the given function g(x) = [tex]3x^2-2x+1[/tex] are as follows:
A) g(0) = 1
B) g(-1) = 6
C) g(3) = 22
D) g(-x) = [tex]3x^2+2x+1[/tex]
E) g(1 - t) = [tex]3t^2-4t+2[/tex]
This values are obtained by substituting x = 0, -1, 3, -x, and (1 - t) respectively in the given function.
What is the function?
A function is the representation of the relation between the output values and the input values. The general form of a function is f(x) = y where x is the independent variable i.e., x: x ∈ R, and y is the dependent variable.
Calculating the function g(x) for the given values of x:
The given values of x are x = 0, -1, 3, -x, and (1 - t)
So, on substituting these values in the given function g(x) = [tex]3x^2-2x+1[/tex], we get
A) At x=0,
g(0) = [tex]3(0)^2-2(0)+1[/tex]
= 1
B) At x=-1
g(-1) = [tex]3(-1)^2-2(-1)+1[/tex]
= 3 + 2 + 1
= 6
C) At x=3
g(3) = [tex]3(3)^2-2(3)+1[/tex]
= 27 -6 + 1
= 22
D) At x= -x,
g(-x) = [tex]3(-x)^2-2(-x)+1[/tex]
= [tex]3x^2+2x+1[/tex]
At x= (1 - t),
g(1 - t) = [tex]3(1 - t)^2-2(1 - t)+1[/tex]
= [tex]3(1-2t+t^2)-2+2t+1[/tex]
= [tex]3-6t+3t^2+2t-1[/tex]
= [tex]3t^2-4t+2[/tex]
Thus, the values for the respective values of x in the given function are calculated by substituting those values in the given function.
Learn more about functions here:
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