Practice — Functions

Easy

If \( f(x) = 3x + 5 \), what is \( f(2) \)?

Easy

Which of the following is NOT a function?

Medium

If \( f(x) = x^2 - 4x + 3 \), find the vertex of the parabola.

Easy

If \( f(x) = \frac{1}{x} \), what is the domain of \( f \)?

Medium

If \( f(x) = 2x + 3 \) and \( g(x) = x^2 \), find \( (f \circ g)(2) \).

Medium

For \( f(x) = \sqrt{5 - x} \), what is the domain?

Hard

If \( f(x) = ax + b \) is invertible and \( f^{-1}(x) = 3x - 4 \), find \( a \) and \( b \).

Hard

Let \( f(x) = x^3 - 3x + 1 \). Find \( f'(x) \) and determine critical points.

Medium

If \( f(x) = \sin x \) and \( g(x) = x^2 \), find \( (g \circ f)(\pi/2) \).

Hard

If \( f: \mathbb{R} \to \mathbb{R} \) is defined by \( f(x) = e^{2x} \), find \( f^{-1}(x) \).

Functions