Which function, h of x, results when f of x equals 2 x squared minus 6 is subtracted from g of x equals 2 x squared plus 5 x minus 1?

Question

Answer options with 5 options
A.
h of x equals 5 x plus 5

B.
h of x equals 5 x minus 7

C.
h of x equals negative 5 x minus 5

D.
h of x equals x squared plus 5 x minus 7

E.
h of x equals 4 x squared plus 5 x minus 7

Answer 1

To find the function \( h(x) \) resulting from subtracting \( f(x) \) from \( g(x) \), we need to evaluate the expression:

\[ h(x) = g(x) - f(x) \]

Given the functions:

• \( f(x) = 2x^2 - 6 \)
• \( g(x) = 2x^2 + 5x - 1 \)

Now, substituting these into our equation:

\[ h(x) = (2x^2 + 5x - 1) - (2x^2 - 6) \]

Now simplifying the expression:

\[ h(x) = 2x^2 + 5x - 1 - 2x^2 + 6 \]

The \( 2x^2 \) terms cancel out:

\[ h(x) = 5x - 1 + 6 \] \[ h(x) = 5x + 5 \]

Thus, the function \( h(x) \) is:

\[ h(x) = 5x + 5 \]

Therefore, the correct answer is:

A. \( h(x) = 5x + 5 \)