Question

If f(x) = 4x2 + 1 and g(x) = x2 – 5, find (f – g)(x)

Answer 1

If f(x) = 4x² + 1 and g(x) = x² – 5, then (f – g)(x) = 3x² + 6

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 :

$( f + g )( x ) = f ( x ) + g ( x )$

$( f - g )( x ) = f ( x ) - g ( x )$

$( f \cdot g )( x ) = f ( x ) \cdot g ( x )$

$\left ( \frac{f}{g} \right )(x) = \frac {f(x)}{g(x)} ~, ~ where ~ g(x) \neq 0$

Let us now tackle the problem!

Given:

$f(x) = 4x^2 + 1$

$g(x) = x^2 - 5$

Unknown:

$(f - g)(x) = ?$

Solution:

$( f - g )( x ) = f ( x ) - g ( x )$

$( f - g )( x ) = (4x^2 + 1) - (x^2 - 5)$

$( f - g )( x ) = 4x^2 + 1 - x^2 + 5$

$\large { \boxed {( f - g )( x ) = 3x^2 + 6} }$

Learn more

• Inverse of Function : brainly.com/question/9289171
• Rate of Change : brainly.com/question/11919986
• Graph of Function : brainly.com/question/7829758

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic , Formula

Answer 2

Answer:

A. 3x² +6

Explanation:

(f-g)(x) = f(x) -g(x) = (4x²+1) -(x²-5) . . . . . substitute the function definitions

... = 4x² +1 -x² +5 . . . . . . . . . . . eliminate parentheses

... = (4-1)x² +(1+5) . . . . . . . . . . . collect like terms

... = 3x² +6