Calculus quiz 24/10/15

What is an inverse function?

• A function that cancels out another function

• A function that reverses the effect of the original function

• A function with the same graph as the original function

• A function that doubles the output values

If f(x) = x³ and f(2) = 8, what is f⁻¹(8)?

• 4

• 2

• 3

• 6

Which function is not one-to-one?

• f(x) = x³

• g(x) = x²

• • h(x) = 2x + 1

• j(x) = ln(x)

All functions have inverses.

• True

• False

What is the inverse function of f(x) = x³ + 2 solved for y?

• y = (x - 2)¹/³

• y = x³ - 2

• y = (x - 2)³

• • None of the above

What is the base of the natural logarithm?

• 10

• e

• 2

• 1

If f(x) = eˣ, what is the inverse function, f⁻¹(x)?

• 1/x

• eˣ

• • ln(x)

• x/e

What does the derivative of a function at a point measure?

• The curvature of the graph

• The maximum value of the function

• The area under the graph

• The slope of the tangent line at that point

Using the definition of derivative, if f(x) = x², what is f'(1)?

• 0

• 1

• 2

• 4

What does the term 'differential calculus' primarily deal with?

• Integrals

• Limits

• Derivatives

• Functions