Skip to main content
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 16
Chapter 5, Problem 16

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)

Verified step by step guidance
1
Identify the function g(x) given as \(g(x) = \left( \frac{1}{4} \right)^x\).
To find \(g(3)\), substitute \(x = 3\) into the function: \(g(3) = \left( \frac{1}{4} \right)^3\).
Rewrite the expression using exponent rules: \(\left( \frac{1}{4} \right)^3 = \frac{1^3}{4^3} = \frac{1}{4^3}\).
Calculate the denominator \$4^3$ by multiplying 4 by itself three times: \(4 \times 4 \times 4\).
Express the final value as a fraction or decimal, then round to the nearest thousandth as required.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

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 finding g(3).
Recommended video:
6:13
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(3), replace x with 3 in g(x) and calculate the result. This process is fundamental for interpreting and solving function-related questions.
Recommended video:
4:26
Evaluating Composed Functions

Rounding to a Specified Decimal Place

Rounding involves adjusting 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. Proper rounding ensures answers are precise and consistent with instructions.
Recommended video:
4:47
The Number e
Related Practice
Textbook Question

Find each value. If applicable, give an approximation to four decimal places. log 0.0022

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. g(2)

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