Question

question 1-4
let $f(x) = x^2 + 4x - 1$ and $g(x) = 2x - 3$. determine $2f(x) - g(x)$.
\\(\circ\\) $2x^2 + 6x + 1$
\\(\circ\\) $2x^2 + 2x - 5$
\\(\circ\\) $-6x^2 + 2x - 5$
\\(\circ\\) $2x^2 - 3$

Explanation:

Step1: Substitute the functions

First, substitute \( f(x) = x^2 + 4x - 1 \) and \( g(x) = 2x - 3 \) into \( 2f(x) - g(x) \). So we have \( 2(x^2 + 4x - 1) - (2x - 3) \).

Step2: Distribute the 2 and the negative sign

Distribute the 2 in \( 2(x^2 + 4x - 1) \) to get \( 2x^2 + 8x - 2 \). Then distribute the negative sign in \( - (2x - 3) \) to get \( -2x + 3 \). Now the expression becomes \( 2x^2 + 8x - 2 - 2x + 3 \).

Step3: Combine like terms

Combine the \( x \)-terms: \( 8x - 2x = 6x \). Combine the constant terms: \( -2 + 3 = 1 \). So the simplified expression is \( 2x^2 + 6x + 1 \).

Answer:

\( 2x^2 + 6x + 1 \) (corresponding to the first option)