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Ch. 4 - Inverse, Exponential, and Logarithmic Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 4 - Inverse, Exponential, and Logarithmic FunctionsProblem 15
Chapter 5, Problem 15

For ƒ(x) = 3x and g(x)= (1/4)x find each of the following. Round answers to the nearest thousandth as needed. g(2)

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Identify the function g(x) given as \(g(x) = \left( \frac{1}{4} \right)^x\).
Substitute the value \(x = 2\) into the function to find \(g(2)\), so write \(g(2) = \left( \frac{1}{4} \right)^2\).
Recall that raising a fraction to a power means raising both numerator and denominator to that power: \(\left( \frac{1}{4} \right)^2 = \frac{1^2}{4^2}\).
Simplify the expression to get \(\frac{1}{16}\).
If needed, convert the fraction to a decimal and round to the nearest thousandth.

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Key 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 and are evaluated by raising the base to the power of the input x. Understanding how to compute values for these functions is essential for solving problems like g(2).
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Exponential Functions

Evaluating Functions at a Given Input

Evaluating a function at a specific input means substituting the input value into the function's formula and simplifying. For example, to find g(2), replace x with 2 in g(x) and calculate the result. This process is fundamental for interpreting and solving function-related questions.
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Rounding Decimal Numbers

Rounding involves approximating a number to a specified decimal place to simplify results. In this problem, answers must be rounded to the nearest thousandth, meaning three digits after the decimal point. Proper rounding ensures clarity and consistency in presenting numerical answers.
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Related Practice
Textbook Question

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 0.8x = 4

Textbook Question

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 4(x-1) = 32x

Textbook Question

Find each value. If applicable, give an approximation to four decimal places. log 63

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)

Textbook Question

Determine whether each function graphed or defined is one-to-one.

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Textbook Question

If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. log5 5 = 1