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 :
\(( f + g )( x ) = f ( x ) + g ( x )\)
\(( f - g )( x ) = f ( x ) - g ( x )\)
\(( f \cdot g )( x ) = f ( x ) \cdot g ( x )\)
\(\left ( \frac{f}{g} \right )(x) = \frac {f(x)}{g(x)} ~, ~ where ~ g(x)
eq 0\)
Let us now tackle the problem!
Given:
\(f(x) = x^2 - 2x\)
\(g(x) = 6x + 4\)
Unknown:
\(x = ?\)
Solution:
\(( f + g )( x ) = f ( x ) + g ( x )\)
\(( f + g )( x ) = (x^2 - 2x) + (6x + 4)\)
\(( f + g )( x ) = x^2 + 4x + 4\)
\(0 = x^2 + 4x + 4\)
\(0 = (x+2)^2\)
\(x + 2 = \sqrt{0}\)
\(\large { \boxed {x = -2} }\)
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
