Question

Let m(x) = Vx+3, n(x) = x3 - 4, and p(x) = 9x - 5,find (m. (n-p))(3).​

Answer 1

SOLUTION

GIVEN

$\sf{m(x) = 5x + 3 \: }$

$\sf{n(x) = {x}^{3} - 4 \: }$

$\sf{p(x) = 9x - 5\: }$

TO DETERMINE

$\sf{(m.(n - p))(3) \: }$

EVALUATION

$\sf{(m.(n - p))(3) \: }$

$= \sf{m(3).(n - p)(3) \: }$

$= \sf{m(3). \bigg(n(3) - p(3) \bigg) }$

Now

$\sf{m(3) \: }$

$\sf{= (5 \times 3) + 3 \: }$

$\sf{ = 15 + 3}$

$= \sf{18 \: }$

Now

$\sf{n(3) \: }$

$\sf{ = {3}^{3} - 4 \: }$

$\sf{ = 27 - 4 \: }$

$\sf{ = 23 \: }$

Again

$\sf{ p(3)\: }$

$\sf{ = (9 \times 5) - 5\: }$

$\sf{ = 45 - 5\: }$

$\sf{ = 40 \: }$

Hence

$\sf{(m.(n - p))(3) \: }$

$= \sf{m(3).(n - p)(3) \: }$

$= \sf{m(3). \bigg(n(3) - p(3) \bigg) }$

$= \sf{18.(23 - 40)}$

$= \sf{18 \times ( - 17) }$

$= \sf{ - 306 }$

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