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3 years ago

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If x = 3 is a zero of the polynomial function f(x) = 2x3 + x2 − 25x + 12, which of the following is another zero of f(x)? ASAP

1 answer:

olasank [31]3 years ago

7 0

If x = 3 is a solution, (x - 3) is a factor of f(x).
2x³ + x² - 25x + 12 ÷ (x - 3) [by long division] = 2x² + 7x - 4
so f(x) = (x - 3)(2x² + 7x - 4)
f(x) = (x - 3)(2x - 1)(x + 4)
so 'zeros', or more correctly solutions, are: x = 3, x = 1/2 and x = -4.
[by setting each of the factors equal to 0 and solving for x].

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4 years ago

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If f (x) = 5 x minus 25 and g (x) = one-fifth x + 5, which expression could be used to verify g(x) is the inverse of f(x)?

gayaneshka [121]

Answer:

$f(g(x))=x$

Step-by-step explanation:

Given a certain function $f(x)$ , and then its inverse function $f^{-1}(x)$ , the following expression is valid:

$(f\cdot f^{-1})(x)=x$

where the expression

$(f\cdot f^{-1})(x)=f(f^{-1}(x))$

indicates the composite function.

In this problem, we have:

$f(x)=5x-25$

And then, its inverse function is

$g(x)=\frac{1}{5}x+5$

To verify that g(x) is the inverse of f(x), the following expression must be true:

$f(g(x))=x$

Substituting the expression of g(x) into f(x), we find that:

$f(g(x))=5g(x)-25=5(\frac{1}{5}x+5)-25=x+25-25=x$

So, g(x) is the inverse of f(x).

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3 years ago

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