Question

use the below functions to answer the following questions.
$f(x) = 6x + 7$ $g(x) = 3x$ $h(x) = 4x^2 + 1$

1. $f(x) + g(x)$
2. $f(x) + h(x)$
3. $g(x) - h(x)$

Explanation:

Step1: Solve \( f(x) + g(x) \)

Substitute \( f(x) = 6x + 7 \) and \( g(x) = 3x \) into \( f(x) + g(x) \).
\( f(x) + g(x) = (6x + 7) + 3x \)
Combine like terms: \( 6x + 3x + 7 = 9x + 7 \)

Step2: Solve \( f(x) + h(x) \)

Substitute \( f(x) = 6x + 7 \) and \( h(x) = 4x^2 + 1 \) into \( f(x) + h(x) \).
\( f(x) + h(x) = (6x + 7) + (4x^2 + 1) \)
Combine like terms: \( 4x^2 + 6x + 7 + 1 = 4x^2 + 6x + 8 \)

Step3: Solve \( g(x) - h(x) \)

Substitute \( g(x) = 3x \) and \( h(x) = 4x^2 + 1 \) into \( g(x) - h(x) \).
\( g(x) - h(x) = 3x - (4x^2 + 1) \)
Distribute the negative sign: \( 3x - 4x^2 - 1 \)
Rearrange terms: \( -4x^2 + 3x - 1 \)

Answer:

1. \( 9x + 7 \)
2. \( 4x^2 + 6x + 8 \)
3. \( -4x^2 + 3x - 1 \)