Test 2 Review

• f⁻¹(x) = -(x-2)/2

• f⁻¹(x) = -2x - 2

• f⁻¹(x) = -x + 2

• f⁻¹(x) = x/2 + 1

Answer explanation

To find the inverse, swap x and y in the equation y = -2x + 2, giving x = -2y + 2. Solving for y yields y = -(x - 2)/2. Thus, the inverse function is f⁻¹(x) = -(x-2)/2, which is the correct choice.

• f⁻¹(x) = 2x - 6

• f⁻¹(x) = 6 - 2x

• f⁻¹(x) = (6+x)/2

• f⁻¹(x) = 2 - x

Answer explanation

To find the inverse, swap x and y in the equation y = (6 - x)/2. This gives x = (6 - y)/2. Solving for y, we get y = 6 - 2x. Thus, the inverse function is f⁻¹(x) = 6 - 2x.

• f⁻¹(x) = (-2/3)x + 1

• f⁻¹(x) = (-3/2)x + 3/2

• f⁻¹(x) = (-2/3)x - 2/3

• f⁻¹(x) = (2/3)x + 2/3

Answer explanation

To find the inverse, swap x and y in the equation y = -1 - (3/2)x, then solve for y. This gives y = (-2/3)x - 2/3, which matches the correct choice: f⁻¹(x) = (-2/3)x - 2/3.

Answer explanation

To find the inverse, swap x and y in the equation y = (8 - x)/2. This gives x = (8 - y)/2. Solving for y, we get y = -2x + 8, which matches the correct choice: f^{-1}(x) = -2x + 8.

Answer explanation

To find the inverse, swap x and y in the equation y = (9 + 5x)/3. Rearranging gives x = (9 + 5y)/3. Solving for y yields f^{-1}(x) = (3x - 9)/5, which matches the correct choice.

• a cubic

• 3

• -7x³

• -7

• -10

• -5x²

• -5

• a quadratic

• not

• 2

Answer explanation

The function h(x) = -5x^2 - 7x^3 - 10 is a cubic polynomial because the highest degree term is -7x³, which has a degree of 3. The leading coefficient is -7, and the constant coefficient is -10.

• -8x^6 - 14x^5 + 5x^3 - 6x^2 - 16x - 1

• -8x^6 - 14x^5 + 5x^3 - 7x^2 - 16x

• -8x^6 - 6x^5 + 5x^3 - 7x^2 - 10x - 1

• -8x^6 - 14x^5 + 5x^3 - 7x^2 - 10x - 1

• -8x^6 - 14x^5 + 5x^3 - 7x^2 - 16x - 1

Answer explanation

Combine like terms: -8x^6 remains, -6x^5 and -8x^5 combine to -14x^5, 5x^3 stays, -8x^2 and x^2 combine to -7x^2, -6x and -10x combine to -16x, and -1 remains. Thus, the correct answer is -8x^6 - 14x^5 + 5x^3 - 7x^2 - 16x - 1.

• +5

• -9

• +6

• -11

• -4

• +9

• +2

Answer explanation

To find the difference, subtract the coefficients of like terms: (7x^4 - 2x^4) = 5x^4, (x^3 - 10x^3) = -9x^3, (9x^2 - 3x^2) = 6x^2, (-3x - 8x) = -11x, and (-1 - 3) = -4. Thus, the answer is +5, -9, +6, -11, -4.

Find the product.

a

b

c

d

e

f

+2x

-6x^2

-8x^2

-3x^3

+4

+16x

-16x

8x^2

• 8

• -

• 5

• +

• -8

Answer explanation

To divide, factor out the common terms: (-72x^2 + 45x) ÷ (-9x) = (72x^2 - 45x) ÷ 9x = 8x - 5. Thus, the answer is 8 - 5.