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Which of these functions are equal/identical? 

 Jun 8, 2019

Best Answer 

 #1
avatar+8215 
+2

\(f(x)\ =\ 6\sqrt{3x}\\~\\ g(x)\ =\ (2x)^4\ =\ 2^4x^4\ =\ 16x^4\\~\\ h(x)\ =\ \big(2^{x+2}\big)^2\ =\ \big(2^{2}\big)^{x+2}\ =\ 4^{x+2}\ =\ 4^2\cdot4^x\ =\ 16\cdot4^x\\~\\ j(x)\ =\ 3\sqrt{12x}\ =\ 3\sqrt{4\cdot3x}\ =\ 3\sqrt{4}\sqrt{3x}\ =\ 6\sqrt{3 x}\\~\\ m(x)\ =\ 16x^4\)

 

So we can see that   \(f(x)\ =\ j(x) \)   and   \(g(x)\ =\ m(x)\)

 

( And  \(h(x)\)  is not equal to any of the other functions. )

 Jun 8, 2019
 #1
avatar+8215 
+2
Best Answer

\(f(x)\ =\ 6\sqrt{3x}\\~\\ g(x)\ =\ (2x)^4\ =\ 2^4x^4\ =\ 16x^4\\~\\ h(x)\ =\ \big(2^{x+2}\big)^2\ =\ \big(2^{2}\big)^{x+2}\ =\ 4^{x+2}\ =\ 4^2\cdot4^x\ =\ 16\cdot4^x\\~\\ j(x)\ =\ 3\sqrt{12x}\ =\ 3\sqrt{4\cdot3x}\ =\ 3\sqrt{4}\sqrt{3x}\ =\ 6\sqrt{3 x}\\~\\ m(x)\ =\ 16x^4\)

 

So we can see that   \(f(x)\ =\ j(x) \)   and   \(g(x)\ =\ m(x)\)

 

( And  \(h(x)\)  is not equal to any of the other functions. )

hectictar Jun 8, 2019

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