Question

evaluate the following functions at x=-3
1. f(×) = x³-64
2.g(×)=|׳-3ײ+3×-1|
3.r(×)=square root of 3-2×
4.q(×)= 3x+1
_____
x²+7x+10​

Answer 1

$1. If \: x = -3 \: then \: the \: value \: of \\f(x) = x^{3} - 64\: is \: f(-3)$

$f(-3) = (-3)^{3} - 64 \\= - 27 - 64\\= -91$

$2. If \: x = -3 \: then \: the \: value \: of \\g(x) = |x^{3}-3x^{2}+3x-1|\: is \: g(-3)$

$g(-3) = |(-3)^{3} - 3(-3)^{2} + 3(-3)-1| \\= | -27-27-9-1| \\= | -64| \\= -(-64) \\ = 64$

$3. If \: x = -3 \: then \: the \: value \: of \\r(x)= \sqrt{3-2^{x}} \:is \: r(-3)$

$r(-3) = \sqrt{ 2 - 3^{-3}} \\= \sqrt{ 2 - \frac{1}{3^{3}}} \\= \sqrt{ 2 - \frac{1}{27}} \\= \sqrt{\frac{ 54-1}{27}} \\= \sqrt{\frac{53}{27}}$

$4. If \: x = -3 \: then \: the \: value \: of\\q(x) = 3x + 1 \: is \: q(-3)$

$q(-3) = 3\times (-3) + 1 \\= -9+1 \\= -8$

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