Hi! I was wondering if anyone might be willing to check my answers for these... I have a suspiscion they are wrong, but I don't have any correct answers to compare them against. If I got them wrong, would you mind giving a brief explanation? Thank you for your help! (x^2-1)+(-2x+3) (I got 2x+x^2+2).
(X^2-1) (x^2+-9) (I got x^3+-12)
(x^2+-9)-(x+-3) (I got x+12)
f(g(x)) F=3x-4 G=(-x^2)I got -3x^3+4x^2
f(g(x))F=-2x G+-2x^2+3 I got 4x^3+-6x
Your answers almost seem like wild guesses. You appear to be in serious need of private tutoring until you grasp basic algebraic rules.
Why do you have both a + and- in front of the 9 in the first problem and in front of the 3 in the second problem?
(x^2-1) (x^2-9) = x^4 - 10x^2 +9
x^2 -9 -(x -3) = x^2 -x -6
If f=3x-4 and g=(-x^2)
f[g(x)] = -3x^2 -4
g[f(x)] = -(3x-4)^2 =-9x^2 +24x -16
Let's evaluate your answers step by step:
1. (x^2 - 1) + (-2x + 3)
To simplify this expression, you need to combine like terms. Start by combining the terms with x^2 and the terms with x:
x^2 - 2x + (-1 + 3)
Adding the constants together:
x^2 - 2x + 2
So, the correct answer is x^2 - 2x + 2.
2. (x^2 - 1)(x^2 - 9)
This is a multiplication of two binomials. You can use the FOIL method to simplify it:
F: x^2 * x^2 = x^4
O: x^2 * (-9) = -9x^2
I: (-1) * x^2 = -x^2
L: (-1) * (-9) = 9
Now add the simplified terms together:
x^4 - 9x^2 - x^2 + 9
Combine like terms:
x^4 - 10x^2 + 9
So, the correct answer is x^4 - 10x^2 + 9.
3. (x^2 - 9) - (x - 3)
Again, you need to combine like terms:
(x^2 - 9) - (x - 3)
Expanding the brackets:
x^2 - 9 - x + 3
Combine like terms:
x^2 - x - 6
So, the correct answer is x^2 - x - 6.
4. f(g(x)), where f(x) = 3x - 4 and g(x) = -x^2
Start by substituting g(x) into f(x):
f(g(x)) = f(-x^2)
Now, replace every occurrence of x in f(x) with -x^2:
f(-x^2) = 3(-x^2) - 4
Simplifying the expression:
-3x^2 - 4
So, the correct answer is -3x^2 - 4.
5. f(g(x)), where f(x) = -2x and g(x) = -2x^2 + 3
Once again, substitute g(x) into f(x):
f(g(x)) = f(-2x^2 + 3)
Replace every occurrence of x in f(x) with (-2x^2 + 3):
f(-2x^2 + 3) = -2(-2x^2 + 3)
Distribute the negative:
4x^2 - 6
So, the correct answer is 4x^2 - 6.
I hope this explanation helps you understand how to evaluate these expressions! Let me know if you have any further questions.