Given-f-x-9-5x-and-f-a-4a-2-find-the-possible-value-of-a-

Question Number 136861 by bramlexs22 last updated on 27/Mar/21

Given f (\sqrt{x + 9}) = 5 x and f (a) = {4 a}^{2}

find the possible value of a .

Answered by EDWIN88 last updated on 27/Mar/21

we have {\begin{cases} a = \sqrt{x + 9}, x = a^{2} - 9 \\ {4 a}^{2} = 5 x, {4 a}^{2} = {5 a}^{2} - 45 \end{cases}

a^{2} = 45, since \sqrt{x + 9} ⩾ 0 for \forall x \in Domain f so

the possible value of a only \sqrt{45} = 3 \sqrt{5}

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