both of these functions grow as x gets larger and larger. which function eventually exceeds the…

Answer:

The function $g(x)=4.2^{x}-5$ eventually exceeds $f(x)=4.2x^{2}-1$.

Explanation:

Step1: Analyze function types

$f(x)$ is a quadratic function, $f(x)=4.2x^{2}-1$. $g(x)$ is an exponential function, $g(x)=4.2^{x}-5$.

Step2: Recall growth - rate property

Exponential functions ($y = a^{x}$, $a>1$) grow faster than polynomial functions as $x$ approaches infinity. Here $a = 4.2>1$ and the polynomial $f(x)$ is of degree 2. So as $x$ gets larger and larger, the exponential function $g(x)=4.2^{x}-5$ will eventually exceed the quadratic function $f(x)=4.2x^{2}-1$.