IB Mathematics Analysis and Approaches Topic AHL…

Consider the function $f(x)=\ln (2 x-1)-\sin (x)$ , where $x>\frac{1}{2}$ .

the graph of $y=f(x)$ for $0.5<x \leq 4$ , showing the intercepts and the behavior at $x=\frac{1}{2}$ .

Let $f(x) = \dfrac{x + 3}{x - 1}$ , for .

Solve $\sqrt{3x+4} \leq 4-x$ for .

Solve $\sqrt{2x+5} \leq 5-x$ for .

Consider the functions $f(x)=\frac{\sin (x)}{x-\pi}$ and , where .

Solve the inequality $\ln (2 x-1)<\sin (x)$ .

Find:

(i) $f(0)$ ;

(ii) the equation of the vertical asymptote of $y = f(x)$ ;

(iii) the equation of the horizontal asymptote of $y = f(x)$ .

Find $f^{-1}(x)$ , stating its domain.

Show that $(f \circ f)(x) = x$ .

the graph of $y = f(x)$ , labelling the intercepts with the axes, the asymptotes, and the line of symmetry.

Find all values of $x$ for which $|f(x)| \leq 1$ .

Find all values of $x$ for which $f(|x|) \leq 1$ .

the graphs of $y=f(x)$ and $y=g(x)$ for $-2 \pi \leq x \leq 2 \pi$ , showing asymptotes and intercepts.

Solve the inequality $f(x)>g(x)$ for $-2 \pi < x < 2 \pi$ . Give answers in radians.

IB Mathematics Analysis and Approaches AHL 2.15—solutions of Inequalities Questionbank