If \( f(x) = x^2 - 3 \), where \( x \) is an integer, which of the following could be a value of \( f(x) \)?

a. 6
b. 0
c. -6

Explain your answer.

f ( x ) = x 2 − 3 a . 6 f ( x ) = 6 6 = x 2 − 3 6 + 3 = x 2
x 2 = 9 x 2 − 9 = 0 ( x − 3 ) ( x + 3 ) = 0 x − 3 = 0 or x + 3 = 0 x = 3 or x = − 3 A n s w er : P oss ib l e .
b . 0 f ( x ) = 0 0 = x 2 − 3 ( x − 3 ​ ) ( x + 3 ​ ) = 0 x − 3 ​ = 0 or \x + 3 ​ = 0
x = 3 ​ or \x = − 3 ​ A n s w er : x i s n o t an in t e g er , n o t p oss ib l e
c . − 6 f ( x ) = − 6 − 6 = x 2 − 3 x 2 = − 6 + 3 x 2 = − 3 A n s w er : s q u a re o f an in t e g er c an n o t b e n e g a t i v e

Answered by Lilith | 2024-06-10

f(x) = x² – 3
If x is an integer, we can substitute values to find which could be a value of f(x).
Let's check the options:
a. f(3) = 3² – 3 = 6
b. f(1) = 1² – 3 = -2
c. f(-1) = (-1)² – 3 = -2
Therefore, 6 could be a value of f(x).

Answered by TimothyJamesCurry | 2024-06-24

The only output from the function f ( x ) = x 2 − 3 that can be reached with integer values is 6. Option b (0) and option c (-6) do not yield integer solutions. Thus, the correct answer is option a: 6.
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Answered by Lilith | 2024-09-03