If f(x) = x² – 2x and g(x) = 6x + 4, the value of x which (f + g)(x) = 0 is -2
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) = x^2 - 2x[/tex]
[tex]g(x) = 6x + 4[/tex]
Unknown:
[tex]x = ?[/tex]
Solution:
[tex]( f + g )( x ) = f ( x ) + g ( x )[/tex]
[tex]( f + g )( x ) = (x^2 - 2x) + (6x + 4)[/tex]
[tex]( f + g )( x ) = x^2 + 4x + 4[/tex]
[tex]0 = x^2 + 4x + 4[/tex]
[tex]0 = (x+2)^2[/tex]
[tex]x + 2 = \sqrt{0}[/tex]
[tex]\large { \boxed {x = -2} }[/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
