(I appreciate help) Rationalize the denominator : 3 * sqrt(2) / (2sqrt(3) - 5sqrt(2) )

1 answer:

3 0

3 √2 3√2(2√3 + 5√2) 30 + 6√6 30 + 6√6
------------- = ----------------------------- = ------------------ = ----------------
2√3 - 5√2 (2√3 - 5√2)(2√3 + 5√2) 12 - 50 -38

-15 - 3√6
= ---------------- answer
19

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Please help ASAP If f(x) = x^2-6x+2 and g(x) =sqrt x find a.) (fog) (x) b.) (gof) (-2)

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$\large\begin{array}{l} \left\{\!\begin{array}{l} \mathsf{f(x)=x^2-6x+2}\\ \mathsf{g(x)=\sqrt{x}}\\ \end{array}\right. \end{array}$

$\large\begin{array}{l} \textsf{a) }\mathsf{(f\circ g)(x)}\\\\ =\mathsf{f\big[g(x)\big]}\\\\ =\mathsf{\big[g(x)\big]^2-6\cdot g(x)+2}\\\\ =\mathsf{\big[\sqrt{x}\big]^2-6\sqrt{x}+2}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(f\circ g)(x)=x-6\sqrt{x}+2} \end{array}}\qquad\checkmark \end{array}$

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$\large\begin{array}{l} \textsf{b) }\mathsf{(g\circ f)(-2)}\\\\ =\mathsf{g\big[f(-2)\big]}\\\\ =\mathsf{\sqrt{f(-2)}}\\\\ =\mathsf{\sqrt{(-2)^2-6\cdot (-2)+2}}\\\\ =\mathsf{\sqrt{4+12+2}}\\\\ =\mathsf{\sqrt{18}}\\\\ =\mathsf{\sqrt{3^2\cdot 2}}\\\\ =\mathsf{3\sqrt{2}}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(g\circ f)(-2)=3\sqrt{2}} \end{array}}\qquad\checkmark \end{array}$

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Tags: composite function composition evaluate algebra

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