# 1)Write the expression 9n^6+7n^3-6 in quadratic form,if possible

A.9(n^3)^3+7n^3-6
B.9(n^2)^3+7(n^2)-6
C.9(n^3)^2+7(n^3)-6
D.not possible
I'm thinking C on this one but im not sure

2)solve b^4+2b^2-24=0
A.-2,-square root of 6,square root of 6,2
B.-square root of 6,2,2i,i square root of 6
C.2,2,-isquare root of 6
D.-2i,2i,- square root of 6,square root of 6

3)If f(x)= x^2+1 and g(x)= x-2,find f[g(x)]
A.x^2-4x+5
B.x^2-1
C.x^2-3
D.x^3-2x^2+x-2

4)Find the inverse of f(x)= 2x-7
=f-1(x)= x+7/2

5)Determine which pair of functions are inverses:
A.f(x)= 3x-1;g(x)= 1/3x-1
B.f(x)= 2x-5;g(x)= x+5/2
C.f(x)= 2x+2;g(x)= 2x-2
D.f(x)= 3x-8;g(x)= 1/3x+8
my answer is D or B

2.) C
3.)A
f[g(x)] = (x-2)^2 + 1
= x^2 -4x +5

4.)correct

5.) B
Follow the same procedure you did for number 4

1. C is right

2. b^4 + 2b^2 - 24 = 0
b^4 + 2b^2 = 24
b^4 + 2b^2 + 1 = 24 + 1
(b^2 + 1)^2 = 25
b^2 + 1 = ± 5
b^2 = 4 or b^2 = -6
b= ±2 or b= ±i√6

3. I got A
f[g(x)]
= f(x-2)
= (x-2)^2 + 1
= x^2 - 4x + 4 + 1
= x^2 - 4x + 5

4. ok if you include brackets as in (x+7)/2

5 ok if you include brackets as in (x+5)/2 and (1/3)(x+8)

1. C
2. A
3. A
4. (x+7)/2
5. B

## 1) The expression is already in quadratic form. So the correct answer is D, not possible.

2) To solve b^4 + 2b^2 - 24 = 0, we can factor it as (b^2 + 6)(b^2 - 4) = 0. Then, solving for b, we get b = ± 2 and b = ± i√6. So the correct answer is B, -√6, 2, 2i, i√6.

3) To find f[g(x)], we substitute g(x) into f(x). So f[g(x)] = (x-2)^2 + 1 = x^2 - 4x + 4 + 1 = x^2 - 4x + 5. Thus, the correct answer is A, x^2 - 4x + 5.

4) To find the inverse of f(x) = 2x - 7, we switch the x and y variables and solve for y. So, x = 2y - 7 ⇒ 2y = x + 7 ⇒ y = (x + 7)/2. Therefore, the inverse of f(x) is f^(-1)(x) = (x + 7)/2. Thus, the correct answer is (x + 7)/2.

5) To check if two functions are inverses, we need to compose them and see if we get the identity function, which is just x. So let's compose f(g(x)) and g(f(x)).

For choice A, f(x) = 3x - 1 and g(x) = (1/3)x - 1. f(g(x)) = 3((1/3)x - 1) - 1 = x - 3 - 1 = x - 4, which is not equal to x. So choice A is not the answer.

For choice B, f(x) = 2x - 5 and g(x) = (1/2)(x + 5). f(g(x)) = 2((1/2)(x + 5)) - 5 = x + 5 - 5 = x, which is equal to x. So choice B is a possible answer.

For choice C, f(x) = 2x + 2 and g(x) = 2x - 2. f(g(x)) = 2(2x - 2) + 2 = 4x - 4 + 2 = 4x - 2, which is not equal to x. So choice C is not the answer.

For choice D, f(x) = 3x - 8 and g(x) = (1/3)x + 8. f(g(x)) = 3((1/3)x + 8) - 8 = x + 24 - 8 = x + 16, which is not equal to x. So choice D is not the answer.

Therefore, the correct answer is B, f(x) = 2x - 5 and g(x) = (1/2)(x + 5) are inverses.

## 1) To write the expression 9n^6 + 7n^3 - 6 in quadratic form, we need to rewrite it in the form ax^2 + bx + c. Since there is no x term, we know that b = 0. The exponent on n^6 is 6, so our leading term will be 9n^6. This means that a = 9. The constant term is -6, so c = -6. Therefore, we can rewrite the expression as 9n^6 + 0n^3 - 6, which simplifies to 9n^6 - 6.

2) To solve the equation b^4 + 2b^2 - 24 = 0, we can first substitute a variable. Let's use x instead of b^2. So we have x^2 + 2x - 24 = 0. Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Factoring gives us (x + 6)(x - 4) = 0. Setting each factor equal to zero, we have x + 6 = 0 or x - 4 = 0. Solving for x, we get x = -6 or x = 4. Since x represents b^2, we take the square root of each solution to find the possible values of b. Therefore, b = -√6, √6, -2, or 2.

3) To find f[g(x)], we substitute g(x) into f(x). Given f(x) = x^2 + 1 and g(x) = x - 2, we replace each occurrence of x in f(x) with g(x). So f[g(x)] becomes (x - 2)^2 + 1. Expanding this expression, we get x^2 - 4x + 4 + 1. Simplifying further, we have x^2 - 4x + 5. Therefore, the correct answer is A.

4) To find the inverse of f(x) = 2x - 7, we need to switch x and y and solve for y. So we have x = 2y - 7. Rearranging the equation, we get 2y = x + 7. Dividing both sides by 2, we have y = (x + 7)/2. Therefore, the inverse of f(x) is equal to f^(-1)(x) = (x + 7)/2.

5) To determine if two functions are inverses, we need to check if the composition of the functions f(g(x)) and g(f(x)) gives us x. Let's check each option:

A)f(x) = 3x - 1; g(x) = 1/3x - 1
f(g(x)) = 3(1/3x - 1) - 1 = 1 - 1 = 0
g(f(x)) = 1/3(3x - 1) - 1 = x - 1 - 1 = x - 2

B)f(x) = 2x - 5; g(x) = x + 5/2
f(g(x)) = 2(x + 5/2) - 5 = 2x + 5 - 5 = 2x
g(f(x)) = (2x - 5) + 5/2 = 2x - 10/2 + 5/2 = 2x - 5/2

C)f(x) = 2x + 2; g(x) = 2x - 2
f(g(x)) = 2(2x - 2) + 2 = 4x - 4 + 2 = 4x - 2
g(f(x)) = 2(2x + 2) - 2 = 4x + 4 - 2 = 4x + 2

D)f(x) = 3x - 8; g(x) = 1/3x + 8
f(g(x)) = 3(1/3x + 8) - 8 = 1 + 8 - 8 = 1
g(f(x)) = 1/3(3x - 8) + 8 = x - 8/3 + 8 = x + 8/3

From the above calculations, we can see that option B, f(x) = 2x - 5; g(x) = x + 5/2, is the only pair of functions in which f(g(x)) = x and g(f(x)) = x. Therefore, the correct answer is B.