# IBDP Maths analysis and approaches Topic: SL 2.9 : The function ax and its graph. HL Paper 1

### Question

On the same set of axes, sketch the graphs of the following two functions f(x) = ax,    -2≤ x ≤ 2 or 2=aand 3. Then complete the table beside.

Ans

### Question

The function f is given by f (x) = 2 – x2 – ex. [Sketch the graph of the function first] Write down (a) the maximum value of f(x).                      …………………………………….. (b) the two roots of the equation f(x) = 0    ……………………………………..

Ans
(a) $$f_{max}=1.17$$ (b) Roots are -1.32, 0.537

### Question

Let $$f(x)=\sqrt{x+1}+1$$ and g(x) = x2. (a) Solve the equation (g0f)(x)=1 (b) Find the function h(x) given that h0f = g (c) Find the function k(x) given that fok = g

Ans
Let $$f(x)=\sqrt {x+1}+1$$ and g(x) = x2. (a) x = -1 (b) h(x) = (x2 – 2x)2 (c) k(x) = x4 – 2x2

### Question

Solve the exponential equations:
(a) $$4^x – 9.2^x + 8 = 0$$    (b) $$3^{2x+2} + 8(3)^{x+1} = 9$$

Ans
(a) x = 0, x = 3       (b) x = -1

### Question

Consider the function f(x) = ex-2.
(a) Find f-1
(b) Sketch the graphs of f and f-1 by indicating clearly any intercepts and asymptotes.

(c) Complete the table