Homework

Problem 1 · easy

Is {(1,2), (3,4), (5,6)} a function? Why?

Problem 2 · easy

Is {(2,3), (2,5), (4,7)} a function? Why?

Problem 3 · easy

Let f(x) = 4x - 5. Find f(3).

Problem 4 · easy

Let f(x) = x^2 + 2x. Find f(-3).

Problem 5 · medium

Let f(x) = 3x - 1. Find f(a + 2).

Problem 6 · easy

Find the domain of f(x) = 1/(x + 7). Write in interval notation.

Problem 7 · easy

Find the domain of f(x) = sqrt(x - 9). Write in interval notation.

Problem 8 · medium

Find the domain of f(x) = sqrt(3 - x). Write in interval notation.

Problem 9 · medium

Find the domain of f(x) = 1/sqrt(x - 4). Write in interval notation.

Problem 10 · medium

Find the domain of g(x) = (x - 1)/((x + 2)(x - 5)). Write in interval notation.

Problem 11 · challenge

Let f(x) = x^2 - 3. Find the difference quotient (f(x+h) - f(x))/h.

Problem 12 · medium

Let f(x) = 2x + 5 and g(x) = x - 3. Find f(g(x)).

Problem 13 · medium

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

Problem 14 · medium

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

Problem 15 · medium

Find the inverse of f(x) = 5x - 3.

Problem 16 · medium

Find the inverse of f(x) = (x + 4)/2.

Problem 17 · easy

Is f(x) = x^3 one-to-one? (Yes or No)

Problem 18 · easy

Is f(x) = x^2 one-to-one on all real numbers? (Yes or No)

Problem 19 · medium

Evaluate f(x) = { 2x if x <= 1; x^2 + 1 if x > 1 } at x = 1.

Problem 20 · medium

Evaluate f(x) = { 2x if x <= 1; x^2 + 1 if x > 1 } at x = 3.

Problem 21 · easy

Let f(x) = x^2 - 4. What are the x-values where f(x) = 0?

Problem 22 · medium

Find the range of f(x) = x^2 + 3 (for all real x). Write in interval notation.

Problem 23 · challenge

Let f(x) = sqrt(x). Find f(f(x)) and simplify.

Problem 24 · challenge

Find the domain of h(x) = sqrt(x^2 - 4). Write in interval notation.

Problem 25 · medium

Let f(x) = 3x + 1. Find f^(-1)(f(5)).