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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 11
Chapter 5, Problem 11

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. ƒ(2)

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Identify the function given: \( f(x) = 3^x \). We need to find \( f(2) \), which means substituting \( x = 2 \) into the function.
Substitute \( x = 2 \) into the function: \( f(2) = 3^{2} \).
Recall the exponent rule: \( a^{n} \) means multiplying the base \( a \) by itself \( n \) times. So, \( 3^{2} = 3 \times 3 \).
Calculate the value of \( 3^{2} \) by multiplying the base by itself the number of times indicated by the exponent.
Round the result to the nearest thousandth if necessary, as the problem instructs.

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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 given x is essential.
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Function Evaluation

Function evaluation involves substituting a specific input value into the function's formula and simplifying to find the output. For example, to find f(2), replace x with 2 and calculate the result.
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Evaluating Composed Functions

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. Here, answers should be rounded to the nearest thousandth, meaning three digits after the decimal point.
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Related Practice
Textbook Question

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

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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. ƒ(-2)

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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. 34 = 81

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Find each value. If applicable, give an approximation to four decimal places. log 0.1

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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. 3x = 7