If f(x) = 3x² + 1 and g(x) = 1 – x, the value of (f – g)(2) is 14
Further explanation
Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.
There are many types of functions in mathematics such as :
- Linear Function → f(x) = ax + b
- Quadratic Function → f(x) = ax² + bx + c
- Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
- Logarithmic function → f(x) = ln x
- Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...
Recall the formulas related to the function such as :
[tex]( f + g )( x ) = f ( x ) + g ( x )[/tex]
[tex]( f - g )( x ) = f ( x ) - g ( x )[/tex]
[tex]( f \cdot g )( x ) = f ( x ) \cdot g ( x )[/tex]
[tex]\left ( \frac{f}{g} \right )(x) = \frac {f(x)}{g(x)} ~, ~ where ~ g(x) \neq 0[/tex]
Let us now tackle the problem!
Given:
[tex]f(x) = 3x^2 + 1[/tex]
[tex]g(x) = 1 - x[/tex]
Unknown:
[tex](f - g)(2) = ?[/tex]
Solution:
[tex]( f - g )( x ) = f ( x ) - g ( x )[/tex]
[tex]( f - g )( x ) = (3x^2 + 1) - (1 - x)[/tex]
[tex]( f - g )( x ) = 3x^2 + x[/tex]
[tex]( f - g )( 2 ) = 3(2)^2 + 2[/tex]
[tex]( f - g )( 2 ) = 12 + 2[/tex]
[tex]\large { \boxed {( f - g )( 2 ) = 14 } }[/tex]
Learn more
- Inverse of Function : https://brainly.com/question/9289171
- Rate of Change : https://brainly.com/question/11919986
- Graph of Function : https://brainly.com/question/7829758
Answer details
Grade: High School
Subject: Mathematics
Chapter: Function
Keywords: Function , Trigonometric , Linear , Quadratic
