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Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 2 - Functions and GraphsProblem 61
Chapter 3, Problem 61

Let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. ƒ-1 (1)

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1
Identify that the notation ƒ¹(1) represents the value of the inverse function of ƒ at 1, meaning we want to find the input x such that ƒ(x) = 1.
Write the equation based on the function ƒ(x) = 2x - 5, setting it equal to 1: 2x - 5 = 1.
Solve the equation for x by first adding 5 to both sides: 2x = 1 + 5.
Then divide both sides by 2 to isolate x: x = \(\frac{1 + 5}{2}\).
The value of x found is ƒ¹(1), which is the output of the inverse function at 1.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Notation and Evaluation

Function notation, such as f(x), represents a rule that assigns each input x to an output. Evaluating a function at a specific value means substituting that value into the function's expression and simplifying to find the output.
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Evaluating Composed Functions

Composite Functions and Inverse Notation

The notation ƒ¹(1) often represents the inverse function evaluated at 1, not the reciprocal. Understanding inverse functions involves finding an input that maps to a given output under the original function.
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Function Composition

Solving Linear Equations

To find ƒ¹(1), you solve the equation f(x) = 1 for x. This requires isolating x by performing algebraic operations, such as addition, subtraction, multiplication, or division, to find the input that produces the output 1.
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Solving Linear Equations with Fractions
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