Let ƒ(x)=x2+3ƒ(x)=$$x^2+3 $$and g(x)=−2x+6g(x)=-2x+6. Find each of the following. See Example 1.(ƒ−g)(4)(ƒ-g)(4)

Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 14

Chapter 3, Problem 14

Let $ƒ (x) = x^{2} + 3$ and $g (x) = - 2 x + 6$ . Find each of the following. See Example 1.
$(ƒ - g) (4)$

Verified step by step guidance

Understand that the expression (ƒ - g)(4) means you need to find the value of the function ƒ(x) minus the function g(x) when x = 4. In other words, (ƒ - g)(4) = ƒ(4) - g(4).

Calculate ƒ(4) by substituting x = 4 into the function ƒ(x) = x^2 + 3. This gives ƒ(4) = 4^2 + 3.

Calculate g(4) by substituting x = 4 into the function g(x) = -2x + 6. This gives g(4) = -2(4) + 6.

Subtract the value of g(4) from ƒ(4) to find (ƒ - g)(4). So, (ƒ - g)(4) = ƒ(4) - g(4).

Simplify the expression from the previous step to get the final value of (ƒ - g)(4).

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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 ƒ(x), represents a rule that assigns each input x to an output value. Evaluating a function at a specific value means substituting that value into the function's expression and simplifying to find the output.

Function Operations (Difference of Functions)

The difference of two functions (ƒ - g)(x) is defined as ƒ(x) minus g(x). This operation creates a new function by subtracting the output of g from the output of ƒ for the same input x.

Substitution and Simplification

To find (ƒ - g)(4), substitute x = 4 into both ƒ(x) and g(x), then subtract the results. Simplifying the expressions after substitution yields the final numerical value.

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