Find the value of f(-2)

Mathematics

1 answer:

ELEN [110]3 years ago

3 0

$f(x)=\left\{\begin{array}{ccc}x^2&if\ x\leq1\\1&if\ 1 \ \textless \ x \leq2\\2-x&if\ 3 \ \textless \ x \leq6\end{array}\right\\\\f(-2)=?\\\\-2\leq1\ therefore\ f(x)=x^2\\\\subtitute\\\\f(-2)=(-2)^2=4$

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sveticcg [70]

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Answer:

9. ±1, ±2, ±3, ±6

11. ±1, ±2, ±3, ±4, ±6, ±12

Step-by-step explanation:

The possible rational roots are (plus or minus) the divisors of the constant term, divided by the divisors of the leading coefficient.

Here, the leading coefficient is 1 in each case, so the possible rational roots are plus or minus a divisor of the constant term.

9. The constant is -6. Divisors of 6 are 1, 2, 3, 6. The possible rational roots are ...

±{1, 2, 3, 6}

11. The constant is 12. Divisors of 12 are 1, 2, 3, 4, 6, 12. The possible rational roots are ...

±{1, 2, 3, 4, 6, 12}

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A graphing calculator is useful for seeing if any of these values actually are roots of the equation. (The 4th-degree equation will have 2 complex roots.)