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

f(3)=g(3)

f(3) < g(3)

f(3) > g(3)

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

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Does (x, y) satisfy the inequality?

Full solution

Q. Given the functions

f(x)=4 x^{4}

and

g(x)=4 \cdot 4^{x}

, which of the following statements is true?

\newline

f(3)=g(3)

\newline

f(3)<g(3)

\newline

f(3)>g(3)

Calculate $f(3)$ : Calculate $f(3)$ using the function $f(x)=4x^{4}$ . $\newline$ $f(3) = 4 \times 3^{4}$ $\newline$ $= 4 \times 81$ $\newline$ $= 324$
Calculate $g(3)$ : Calculate $g(3)$ using the function $g(x)=4\cdot4^{(x)}$ . $g(3) = 4 \cdot 4^{3} = 4 \cdot 64 = 256$
Compare values: Compare the values of $f(3)$ and $g(3)$ to determine which statement is true. $\newline$ Since $f(3) = 324$ and $g(3) = 256$ , it is clear that f(3) > g(3).

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