Question

For the function $$ f(x)=x^{2}-1 $$ a student claimed that $f(-1)=-2$. This is incorrect. WHAT WENT WRONG? Find the correct value of $f(-1)$.

   For the function
$$
f(x)=x^{2}-1
$$
a student claimed that $f(-1)=-2$.
This is incorrect. WHAT WENT WRONG?
Find the correct value of $f(-1)$.

Algebra for College Students

Algebra for College Students

Margaret L. Lial,… 9th Edition

Chapter 4, Problem 8

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For the function $$ f(x)=x^{2}-1 $$ a student claimed that $f(-1)=-2$. This is incorrect. WHAT WENT WRONG? Find the correct value of $f(-1)$.

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Key Concepts

Function Evaluation

Evaluating a function involves substituting a specific input value into the function's formula and simplifying the expression according to the defined operations. This process must follow the function's definition carefully.

Substitution and Simplification

After substitution, the next step is to perform algebraic manipulations and simplifications correctly. This includes correctly applying mathematical operations to arrive at the proper result.

Order of Operations

The order of operations (PEMDAS/BODMAS) must be strictly followed when simplifying expressions. In particular, exponentiation must be performed before addition or subtraction, ensuring that terms like x² are correctly computed before further operations.

Handling of Negative Numbers in Exponentiation

When squaring a negative number, it is important to recognize that the square of a negative number is positive. For example, (-1)² equals 1, not -1. Misapplying this rule can lead to incorrect results, such as mistakenly calculating f(-1) = -2 instead of 0.

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