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Given the functions f(x)=2x^(4) and g(x)=8*3^(x), which of the following statements is true? f(6) < g(6) f(6) > g(6) f(6)=g(6)

Given the functions f(x)=2x4 f(x)=2 x^{4} and g(x)=8⋅3x g(x)=8 \cdot 3^{x} , which of the following statements is true?\newlinef(6)<g(6) f(6)<g(6) \newline=""f(6)="">g(6)="" f(6)="">g(6) \newlinef(6)=g(6) f(6)=g(6)

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Full solution

Q. Given the functions f(x)=2x4 f(x)=2 x^{4} and g(x)=8⋅3x g(x)=8 \cdot 3^{x} , which of the following statements is true?\newlinef(6)<g(6) f(6)<g(6) \newlinef(6)>g(6) f(6)>g(6) \newlinef(6)=g(6) f(6)=g(6)
  1. Calculate f(6)f(6): Calculate f(6)f(6) using the function f(x)=2x4f(x) = 2x^4.f(6)=2×(64)=2×(1296)=2592f(6) = 2\times(6^4) = 2\times(1296) = 2592
  2. Calculate g(6)g(6): Calculate g(6)g(6) using the function g(x)=8⋅3xg(x) = 8\cdot3^x.g(6)=8⋅(36)=8⋅(729)=5832g(6) = 8\cdot(3^6) = 8\cdot(729) = 5832
  3. Compare values: Compare the values of f(6)f(6) and g(6)g(6).\newlineSince f(6)=2592f(6) = 2592 and g(6)=5832g(6) = 5832, it is clear that f(6) < g(6).

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