Answer:
a. 29
b. g(p) = 2p² -3
c. 4x +2h
Step-by-step explanation:
You want to evaluate g(x) = 2x²-3 for different values of x.
a. x = -4
Substituting -4 for x, we have ...
[tex]g(-4)=2(-4)^2-3 =2(16)-3\\\\\boxed{g(-4)=29}[/tex]
b. x = p
Substituting p for x, we have ...
[tex]\boxed{g(p)=2p^2-3}[/tex]
c. Difference quotient
The given expression simplifies to ...
[tex]\dfrac{g(x+h)-g(x)}{h}=\dfrac{(2(x+h)^2-3)-(2x^2-3)}{h}\\\\=\dfrac{2(x^2+2hx+h^2))-3-2x^2+3}{h}=\dfrac{2x^2+4hx+2h^2-3-2x^2+3}{h}\\\\=\boxed{4x+2h}[/tex]
__
Additional comment
The square of a real number is always positive. That should be your first clue that (-4)² = 16 ≠ -16.
Sometimes it helps to remember that an exponent signifies repeated multiplication:
(-4)² = (-4)(-4) . . . . . . has an even number of minus signs, so is positive.
Please note that this is different from -4² = -(4²) = -16.
