Textbook Question
For ƒ(x) = 3x and g(x)= (1/4)x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(-3)
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6. Exponential & Logarithmic Functions
Introduction to Exponential Functions
1:38 minutesProblem 26
Textbook Question
For ƒ(x) = 3x and g(x)= (1/4)x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(2.34)
Verified step by step guidance1
Identify the function g(x) given as \(g(x) = \left( \frac{1}{4} \right)^x\).
Substitute the given value \(x = 2.34\) into the function: \(g(2.34) = \left( \frac{1}{4} \right)^{2.34}\).
Rewrite the expression if needed, recognizing that \(\frac{1}{4} = 4^{-1}\), so \(g(2.34) = 4^{-2.34}\).
Use a calculator to evaluate \$4^{-2.34}$, which involves calculating the power of a number with a decimal exponent.
Round the result to the nearest thousandth as instructed.
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponential Functions
Exponential functions have the form f(x) = a^x, where the base a is a positive constant. They model growth or decay processes depending on whether the base is greater than or less than 1. Understanding how to evaluate these functions for any real number x is essential.
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Evaluating Functions at a Given Input
To find the value of a function at a specific input, substitute the input value into the function's formula and simplify. This process often involves calculating powers or roots, especially for exponential functions, and may require a calculator for non-integer exponents.
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Rounding to a Specified Decimal Place
Rounding is the process of limiting a number to a certain number of decimal places for simplicity or clarity. In this problem, answers must be rounded to the nearest thousandth, meaning three digits after the decimal point, which requires understanding place value and rounding rules.
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