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Given the functions f(x)=4x and g(x)=9*2^(x), which of the following statements is true? f(2) < g(2) f(2)=g(2) f(2) > g(2)

Given the functions f(x)=4x f(x)=4 x and g(x)=9⋅2x g(x)=9 \cdot 2^{x} , which of the following statements is true?\newlinef(2)<g(2) f(2)<g(2) \newline=""f(2)="g(2)">g(2)="" f(2)="g(2)">g(2)

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Full solution

Q. Given the functions f(x)=4x f(x)=4 x and g(x)=9⋅2x g(x)=9 \cdot 2^{x} , which of the following statements is true?\newlinef(2)<g(2) f(2)<g(2) \newlinef(2)=g(2) f(2)=g(2) \newlinef(2)>g(2) f(2)>g(2)
  1. Calculate f(2)f(2): Calculate f(2)f(2) using the function f(x)=4xf(x) = 4x.\newlinef(2)=4×2f(2) = 4 \times 2\newlinef(2)=8f(2) = 8
  2. Calculate g(2)g(2): Calculate g(2)g(2) using the function g(x)=9×2xg(x) = 9 \times 2^x.
    g(2)=9×22g(2) = 9 \times 2^2
    g(2)=9×4g(2) = 9 \times 4
    g(2)=36g(2) = 36
  3. Compare values: Compare the values of f(2)f(2) and g(2)g(2).\newlineSince f(2)=8f(2) = 8 and g(2)=36g(2) = 36, it is clear that f(2) < g(2).

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