2.1 Basic functions (in class)

Which of the following function(s) is/are one-to-one?

If [math]f(x)=x^2+3[/math], which of the following is true?

If [math]f(x)=\dfrac{2021}{x+2021}[/math], which of the following is true?

The table below shows some functions values of [math]f(x)[/math] and [math]g(x)[/math]

Evaluate:
(a) [math](f\circ g\circ f)(1)[/math]
(b) [math]g(f(3)-1)[/math]
(c) [math]f(f(f(2)))[/math]

If [math]f(x)=2024(x-2025)+2026[/math], what is the value of [math]\dfrac{f(1026)-f(1024)}{2}[/math]?

Let [math]f(x)[/math] be a function satisfying [math]f(x+3)=2f(x)+1[/math]. Suppose the [math]x[/math]-intercept of [math]f(x)[/math] is 2. Find [math]f(11)[/math].

The figure below shows the graph of function [math]f(x)[/math]. The domain of [math]f(x)[/math] is [math][-6,6][/math] and [math]f(-1.5)=2[/math].

(a) Find all possible values of [math]m[/math] such that [math]f(m)=3[/math]. Write your answers in ascending order.

(b) Find the conditions of [math]k[/math] such that the equation [math]f(x)=k[/math] has 4 solutions.

(c) Evaluate [math]f(f(5))[/math].

(d) If [math]g(x)[/math] is a linear function and [math]g(x)[/math] and [math]f(x)[/math] have common [math]x[/math]-intercept and [math]y[/math]-intercept, what is the equation of [math]g(x)[/math]?

(e) Find the domain of [math]f(g(x))[/math].

(f) Solve the inequality [math]f(x)<g(x)[/math].

Let [math]f(x)[/math] be a linear function satisfying [math]f(2a+3)=4a-7[/math]. What is the summation of the slope and the [math]y[/math]-intercept of [math]f(x)[/math]?

If [math]f(x)=\sqrt{x+2}[/math] and [math]g(x)=\dfrac{1}{x}[/math], which of the following functions domains differs from the others?

If [math]f(x)=\dfrac{3}{\sqrt{1-x}}[/math], which of the following statements is true?

If [math]f(x)=f(x)=3(3|3x|)^3+3[/math], what is the range of [math]f(x)[/math]?

Let [math]f(x)=-2|x|+3[/math] and [math]g(x)=\sqrt{x}-5[/math].

(a) Evaluate [math]f(g(4))[/math].

(b) Find the [math]x[/math]-intercept(s) of [math]f(g(x))[/math]. If you have two or more answers, write the smallest one.