What does it mean when a function is one-to-one?
1 answer:
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First, we could try to factorize the polynomial. We could group the first and third terms, and the second and fourth term:
Now, x(x^2-9) is a common factor:
.
By the difference of squares formula, our final factorization is :
x(3x-1)(x-3)(x+3).
Here we can see clearly that the roots of f(x) are 0, 1/3, 3, and -3.
Remark: we grouped the terms in pairs as we did, noticing that the ratio of the exponents, and coefficient in each pair was the same.
Answer: 0, 1/3, 3, and -3.
Now, x(x^2-9) is a common factor:
By the difference of squares formula, our final factorization is :
x(3x-1)(x-3)(x+3).
Here we can see clearly that the roots of f(x) are 0, 1/3, 3, and -3.
Remark: we grouped the terms in pairs as we did, noticing that the ratio of the exponents, and coefficient in each pair was the same.
Answer: 0, 1/3, 3, and -3.