Question

question 4 of 10
if $f(x) = 4x^2 - 3$ and $g(x) = x + 1$, find $(f - g)(x)$.

a. $4x^2 - x - 4$

b. $x - 4x^2 - 2$

c. $4x^2 - x - 2$

d. $4x^3 - 3$

Explanation:

Step1: Recall the definition of function subtraction

To find \((f - g)(x)\), we use the formula \((f - g)(x)=f(x)-g(x)\).
Given \(f(x) = 4x^{2}-3\) and \(g(x)=x + 1\), substitute these into the formula:
\((f - g)(x)=(4x^{2}-3)-(x + 1)\)

Step2: Distribute the negative sign

Distribute the negative sign to each term in \(g(x)\):
\((f - g)(x)=4x^{2}-3 - x - 1\)

Step3: Combine like terms

Combine the constant terms \(-3\) and \(-1\):
\(4x^{2}-x+(-3 - 1)=4x^{2}-x - 4\)

Answer:

A. \(4x^{2}-x - 4\)