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# Evaluating Functions

Evaluating a function means finding the output value (or result) of the function when a specific input value (or argument) is given.

• Evaluating Functions
• Formula for Evaluating Functions
• Solved Examples of Evaluating Function
• FAQs

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## Evaluating Functions

The process of evaluating a function involves substituting the input value for the function’s variable and simplifying the resulting expression.

For example, consider the function f(x) = 2x + 1. To evaluate the function at x = 3, we substitute 3 for x and simplify:

f(3) = 2(3) + 1 = 6 + 1 = 7

So, the value of the function f(x) when x = 3 is 7.

Similarly, consider the function g(x) = x^2 – 4x + 3. To evaluate the function at x = 2, we substitute 2 for x and simplify:

g(2) = 2^2 – 4(2) + 3 = 4 – 8 + 3 = -1

So, the value of the function g(x) when x = 2 is -1.

In general, to evaluate a function f(x) at a given value of x, substitute the value of x into the function and simplify the resulting expression to get the output value of the function.

## Formula for Evaluating Functions

The formula for evaluating a function at a specific value of its independent variable is:

f(x) = function expression To evaluate the function at a specific value, simply replace x in the function expression with the value you want to evaluate it at, and simplify the resulting expression.

For example, let’s say we want to evaluate the function f(x)= x^2 + 4x- 5 at x=4
f(4) = 4^4 + 3 (4) – 5
= 256 + 12 – 5
=264

So, the value of function f(x) at x = 4 is 264.

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## Solved Examples of Evaluating Function

Example 1: Evaluate the function f(x) = 3x – 4 at x = 5.

Solution: Using the formula for evaluating functions, we substitute x = 5 into the function expression and simplify:

f(5) = 3(5) – 4
= 15 – 4
= 11

Therefore, the value of the function f(x) at x = 5 is 11.

Example 2: Evaluate the function g(x) = 2x^2 + 5x – 3 at x = -2.

Solution: Using the formula for evaluating functions, we substitute x = -2 into the function expression and simplify:

g(-2) = 2(-2)^2 + 5(-2) – 3
= 2(4) – 10 – 3
= 8 – 10 – 3
= -5

Therefore, the value of the function g(x) at x = -2 is -5.

Example 3: Evaluate the function h(x) = sqrt(x + 4) – 2 at x = 3.

Solution: Using the formula for evaluating functions, we substitute x = 3 into the function expression and simplify:

h(3) = sqrt(3 + 4) – 2
= sqrt(7) – 2

Therefore, the value of the function h(x) at x = 3 is sqrt(7) – 2.

These are some examples of evaluating functions.

## Evaluating Functions FAQS

##### What is a function?

A function is a mathematical object that takes an input value, called the argument, and produces an output value, called the function value or the result. A function can be thought of as a rule that assigns each input value to a unique output value.

##### How do I evaluate a function?

To evaluate a function at a specific value of its independent variable, substitute the value of the variable into the function expression and simplify the resulting expression to get the output value of the function.

##### What is the domain of a function?

The domain of a function is the set of all possible input values (or arguments) for which the function is defined. It is the set of values that can be plugged into the function without causing any mathematical inconsistencies or undefined results.

##### What is the range of a function?

The range of a function is the set of all possible output values (or results) that the function can produce for the input values in its domain. It is the set of values that the function can take on.

##### What is a one-to-one function?

A one-to-one function is a function that maps each input value to a unique output value, and no two different input values are mapped to the same output value. In other words, the function never assigns the same output value to two different input values.

##### What is an inverse function?

An inverse function is a function that undoes the action of another function. If f(x) is a function, then its inverse function f^-1(x) is a function that takes the output value of f(x) as its input and produces the input value of f(x) as its output. In other words, f^-1(f(x)) = x for all x in the domain of f(x). Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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