For the function defined by f(x)=3x^2+5x+2, find the following values.
(a) f(-4)=
(b) f(-x)=
(c) -f(x)=
(d) f(x+h)=
just plug and chug:
f(-4) = 3(16)+5(-4)+2 = 30
f(-x) = 3(-x)^2+5(-x)+2 = 3x^2-5x+2
-f(x) = -(3x^2+5x+2) = -3x^2-5x-2
f(x+h) = 3(x+h)^2+5(x+h)+2
= 3x^2+6hx+3h^2 + 5x+5h + 2
= 3x^2 + (6h+5)x + (3h^2+5h+2)
To find the values for the function f(x) = 3x^2 + 5x + 2, we simply substitute the given values into the function expression and simplify.
(a) f(-4):
To find f(-4), substitute -4 for x in the expression:
f(-4) = 3(-4)^2 + 5(-4) + 2
We start by evaluating the exponent:
f(-4) = 3(16) + 5(-4) + 2
Next, we perform the multiplications and additions:
f(-4) = 48 - 20 + 2
Finally, we combine like terms to get the final answer:
f(-4) = 30
So, f(-4) is equal to 30.
(b) f(-x):
To find f(-x), substitute -x for x in the expression:
f(-x) = 3(-x)^2 + 5(-x) + 2
We start by evaluating the exponent:
f(-x) = 3x^2 + 5(-x) + 2
Next, we simplify the expression:
f(-x) = 3x^2 - 5x + 2
So, f(-x) is equal to 3x^2 - 5x + 2.
(c) -f(x):
To find -f(x), we need to multiply f(x) by -1:
-f(x) = -1 * (3x^2 + 5x + 2)
Next, distribute the negative sign to each term:
-f(x) = -3x^2 - 5x - 2
So, -f(x) is equal to -3x^2 - 5x - 2.
(d) f(x+h):
To find f(x+h), substitute (x+h) for x in the expression:
f(x+h) = 3(x+h)^2 + 5(x+h) + 2
We start by evaluating the exponent:
f(x+h) = 3(x^2 + 2xh + h^2) + 5(x+h) + 2
Next, we simplify the expression by distributing:
f(x+h) = 3x^2 + 6xh + 3h^2 + 5x + 5h + 2
So, f(x+h) is equal to 3x^2 + 6xh + 3h^2 + 5x + 5h + 2.