Algebra and functions

Question 1 of 10

Find the remainder when 2x³ + x − 3 is divided by (x + 1).

Question 2 of 10

Solve 3^(2x) = 27.

Question 3 of 10

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

Question 4 of 10

Solve 2 log₃ x − log₃(x − 2) = 2.

Question 5 of 10

If f(x) = 2x + 3, find f⁻¹(x).

Question 6 of 10

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

Question 7 of 10

Solve the equation 2^(2x) − 5(2^x) + 4 = 0.

Question 8 of 10

Find the sum to infinity of the geometric series 8 + 4 + 2 + …

Question 9 of 10

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

Question 10 of 10

Express (3x + 1)/((x − 1)(x + 2)) in partial fractions. The coefficient over (x − 1) is