Algebra and functions

Question 1 of 10

Find the remainder when 3x³ − 2x² + x − 5 is divided by 3x − 2.

Question 2 of 10

The remainder when x³ − 2x + 5 is divided by (x − 1) is

Question 3 of 10

Solve log₃ (x + 1) = 2.

Question 4 of 10

The inverse of f(x) = (2x + 1)/(x − 3), x ≠ 3, is

Question 5 of 10

If f(x) = (2x + 1)/(x − 3), x ≠ 3, find f⁻¹(x).

Question 6 of 10

If f(x) = x² − 1 and g(x) = 2x + 3, find (f ∘ g)(−1).

Question 7 of 10

For what values of k does x² + kx + 9 = 0 have equal roots?

Question 8 of 10

Express (5x + 1)/((x + 1)(x − 1)) in partial fractions.

Question 9 of 10

Find the sum of the roots of 2x² − 7x + 3 = 0.

Question 10 of 10

Find the domain of f(x) = √(4 − x²).