Question

f(x) = 8x - 2\
g(x) = 9x + 2\
what is h(x) = f(x) - g(x)?\
\
\bigcirc\\ h(x) = 17x + 14\
\bigcirc\\ h(x) = x + 4\
\bigcirc\\ h(x) = -x - 4\
\bigcirc\\ h(x) = -x + 14

Explanation:

Step1: Substitute the functions

Substitute \( f(x) = 8x - 2 \) and \( g(x) = 9x + 2 \) into \( h(x)=f(x)-g(x) \).
\( h(x)=(8x - 2)-(9x + 2) \)

Step2: Distribute the negative sign

Distribute the negative sign to the terms inside the second parentheses.
\( h(x)=8x - 2 - 9x - 2 \)

Step3: Combine like terms

Combine the \( x \)-terms and the constant terms.
For \( x \)-terms: \( 8x-9x=-x \)
For constant terms: \( -2 - 2=-4 \)
So, \( h(x)=-x - 4 \)

Answer:

\( h(x)=-x - 4 \) (corresponding to the option "h(x) = -x - 4")