If f(x) = x^2 - px - 4 and f(3) = 7, what is the value of p?

To find the value of ( p ) in the function ( f(x) = x^2 - px - 4 ) given that ( f(3) = 7 ), we start by substituting 3 into the function.

Calculate ( f(3) ):

[

f(3) = 3^2 - p(3) - 4

]

[

f(3) = 9 - 3p - 4

]

[

f(3) = 5 - 3p

]

Since we know that ( f(3) = 7 ), we can set up the equation:

[

5 - 3p = 7

]

To solve for ( p ), first subtract 5 from both sides:

[

-3p = 7 - 5

]

[

-3p = 2

]

Now, divide both sides by -3:

[

p = -\frac{2}{3}

]

Thus, the correct value of ( p ) is (-\frac{2}{3}).

This matches the first answer choice, confirming that it is indeed correct. The steps