Answer:
a. f(0) = -6
b. f(2) =10
c. f(-4) = 32
d. f(b) = 3b^2+2b-6
e. f(4a) = 48a^2+8a-6
The function values for the function f(x) = 3x² + 2x - 6, for the values are:
a. f(0) = -6
b. f(2) = 10
c. f(-4) = 34
d. f(b) = 3b² + 2b - 6
e. f(4a) = 48a² + 8a - 6
To calculate function value f(k) for a function f(x), we substitute variable x = k, in the function f(x).
In the question, we are asked to find the function value for the function f(x) = 3x² + 2x - 6 for:
a. f(0)
b. f(2)
c. f(-4)
d. f(b)
e. f(4a).
We calculate these in the following ways:-
a. f(0):
We substitute the value of x = 0 in the function f(x).
Therefore f(0) = 3(0)² + 2(0) - 6,
or, f(0) = 0 + 0 - 6 = -6.
Therefore, the function value f(0) for the function f(x) = 3x² + 2x - 6 is -6.
b. f(2):
We substitute the value of x = 2 in the function f(x).
Therefore f(2) = 3(2)² + 2(2) - 6,
or, f(2) = 12 + 4 - 6 = 10.
Therefore, the function value f(2) for the function f(x) = 3x² + 2x - 6 is 10.
c. f(-4):
We substitute the value of x = -4 in the function f(x).
Therefore f(-4) = 3(-4)² + 2(-4) - 6,
or, f(-4) = 48 - 8 - 6 = 34.
Therefore, the function value f(-4) for the function f(x) = 3x² + 2x - 6 is 34.
d. f(b):
We substitute the value of x = b in the function f(x).
Therefore f(b) = 3(b)² + 2(b) - 6,
or, f(b) = 3b² + 2b - 6.
Therefore, the function value f(b) for the function f(x) = 3x² + 2x - 6 is 3b² + 2b - 6.
e. f(4a):
We substitute the value of x = 4a in the function f(x).
Therefore f(4a) = 3(4a)² + 2(4a) - 6,
or, f(0) = 48a² + 8a - 6.
Therefore, the function value f(0) for the function f(x) = 3x² + 2x - 6 is 48a² + 8a - 6.
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