Given the function rule f(x) = x2 – 3x + 2, what is the output of f(-2)?

Statistics are divided into several branches. The section that controls numbers and their calculation is arithmetic, used for numerical calculations such as addition, subtraction, multiplication, and division. Geometry is about studying the shape and size and their construction. Algebra is another interesting branch of mathematics in which alphabetical characters are used for the calculation of unknowns. Just like arithmetic, algebra also contains all the different types of mathematical operators. 

Solution: 

In the given algebraic expression, we have to find out the value at x= (2)

Algebraic Expressions

In an algebraic expression, we use numerals and variables. The symbol which has a fixed numerical value is termed as ‘constant’ and the symbol which can take any numerical value is termed as ‘variable’. Numerals are basically constant because they have fixed values but variables are not fixed and represented by an alphabet. Numerals and variables are connected by different mathematical operators are known as algebraic expressions. 

For example, 5 and 6 are numerals and x is a variable, connected together to form an algebraic expression 5x + 6, consisting of two-term 5x and 6. On the basis of the number of them, the algebraic expression is divided into the following categories.

• Monomial: An algebraic expression having only one term is known as a monomial. Example: 5x, 6y, etc
• Binomial: An algebraic expression having two terms is known as binomial. Example: 5x + 2, 3y + 5x, etc
• Trinomial: An algebraic expression having three terms is known as trinomial. Example: 3x + 2y + 9z, 2a + 3b + 5c, etc
• Polynomial: An algebraic expression that has one or more than one term is known as a polynomial.

Value of an algebraic expression

An algebraic expression is the combination of numerals and variables. To find the value of an algebraic expression the value of variables should be known.

Steps to find out the value of an algebraic expression

• Step 1: In the given algebraic expression, replace the value of the variable with its given numerical value.
• Step 2: Solve the terms by using mathematical operations.
• Step 3: Simply the arithmetic expression.

Given the function rule f(x) = x² – 3x + 2, what is the output of f(-2)?

Solution: 

In the given algebraic expression, we have to find out the value at x = (-2)

Step 1: Put x = (-2) in the given function.

f(-2) = (-2)² – 3 × (-2) + 2

Step 2: Solve the terms.

f(-2) = (-2) × (-2) – 3 × (-2) +2

= 4 + 6 +2

Step 3: Solve the arithmetic expression.

f(-2) = 4 + 6 + 2

= 12

So the output of given function rule f(x) = x² – 3x + 2 at  f(-2) is 12.

Similar Questions

Question 1: Given the function rule f(x) = x³ – 3x² +12, what is output at f(2)

Solution:

Step 1: Put x = (2) in the given function.

f(2) = (2)³ – 3(2)² +12

Step 2: Solve the term.

f(2) = 2 × 2 × 2 – 3 × 2 × 2 +12

= 8 – 12 +12

Step 3: Solve the arithmetic expression.

f(2) = 8 – 12 + 12

= 20 – 12 

= 8

So the output of given function rule f(x) = x³ – 3(x)² +12 at f(2) is 8.

Question 2: Given the function rule f(y) = y² – 9y +13, what is output at f(-3)?

Solution:

 In the given algebraic expression, we have to find out the value at y = (-3)

Step 1: Put y = (-3) in the given algebraic expression.

f(-3) = (-3)² – 9(-3) +13

Step 2: Solve the term.

f(-3) = (-3) × (-3) – 9 × (-3) +13

= 9 +21 +13

Step 3: Solve the arithmetic expression.

f(-3) = 9 +21 +13

= 43

So output of given function rule f(y) = y² – 9y +13 at f(-3) is 43.