Homework

Problem 1 · medium

Let f(x) = 2x^2 + 1. Find f(x+h).

Problem 2 · medium

Let f(x) = 2x^2 + 1. Find (f(x+h) - f(x))/h and simplify.

Problem 3 · medium

Let f(x) = 3x - 5. Find (f(x+h) - f(x))/h.

Problem 4 · easy

Solve by factoring: x^2 - 11x + 28 = 0

Problem 5 · medium

Solve using the quadratic formula: x^2 - 4x - 1 = 0

Problem 6 · medium

Complete the square: x^2 - 8x + 10. Write in vertex form.

Problem 7 · medium

Solve: x^2 + 2x = 8 by completing the square.

Problem 8 · medium

Factor completely: x^4 - 16

Problem 9 · challenge

Simplify: (f(x+h)-f(x))/h for f(x) = x^3, factor and cancel h.

Problem 10 · challenge

Simplify the complex fraction: (1/(x+h)^2 - 1/x^2) / h

Problem 11 · medium

Find the domain of f(g(x)) where f(x) = sqrt(x) and g(x) = x - 5.

Problem 12 · challenge

Find the domain of f(g(x)) where f(x) = 1/(x-2) and g(x) = sqrt(x).

Problem 13 · medium

Where is (x + 1)/(x - 3) > 0? Write in interval notation.

Problem 14 · medium

Where is x^2 - 5x + 6 > 0? Write in interval notation.

Problem 15 · medium

Solve |2x - 5| <= 7 and write in interval notation.

Problem 16 · challenge

Solve e^(2x) - 5e^x + 6 = 0 by substituting u = e^x.

Problem 17 · challenge

Simplify: (sqrt(x+h) - sqrt(x))/h by rationalizing the numerator.

Problem 18 · challenge

Factor: x^6 - 64

Problem 19 · easy

Evaluate f(f(2)) for f(x) = 3x - 1.

Problem 20 · medium

Solve: 3(x+2)^2 - 27 = 0

Problem 21 · medium

Simplify: (x^2 - 4)/(x^2 - 4x + 4)

Problem 22 · medium

Solve: log_2(x^2 - 2x) = 3

Problem 23 · medium

Find the x-intercepts of f(x) = 2x^2 - 7x - 15.

Problem 24 · challenge

Rationalize the numerator: (sqrt(x) - 3)/(x - 9)

Problem 25 · challenge

Given f(x) = x/(x-1), find and simplify f(f(x)).