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# Which of these functions are equal/identical?

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Which of these functions are equal/identical?

Jun 8, 2019

#1
+8759
+3

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

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
+8759
+3

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

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