Question

If $f(x)=x^{2}+4 x+3$, find $f(a-1)$ and $f(a-2)$.

   If $f(x)=x^{2}+4 x+3$, find $f(a-1)$ and $f(a-2)$.

Calculus and Its Applications

Calculus and Its Applications

Larry J. Goldstein,… 13th Edition

Chapter 0, Problem 18

Instant Answer

Solved by Expert Carson Merrill

08/30/2021

Step 1

So, $f(a-1) = (a-1)^{2}+4(a-1)+3$. Show more…

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If $f(x)=x^{2}+4 x+3$, find $f(a-1)$ and $f(a-2)$.

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Key Concepts

Function Evaluation

Function evaluation is the process of determining the output of a function for a given input. This involves substituting the input value into the function’s expression in place of the variable, and then carrying out the necessary arithmetic operations to find the result.

Substitution

Substitution in algebra refers to replacing a variable with an expression or a value. When evaluating a function at a certain input, substitution is performed by replacing the variable with the provided expression before simplifying the result.

Polynomial Expansion

Polynomial expansion involves multiplying and simplifying expressions that include powers and products of variables. This process typically uses the distributive property to expand the expression fully, combining like terms if needed.

Algebraic Simplification

Algebraic simplification is the procedure of reducing an expression to its simplest form by performing arithmetic operations and combining like terms. This step is essential to clearly express the final answer in a neat and concise manner.

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