# Problem Statement## a. Draw one graph of a function \( f \) that satisfies all six of the following properties:1. **Domain of \( f \) is all reals.**2. **Range of \( f \) is all reals \(\leq 5\).**3. **\( f(3) = 2 \)**4. **\( f(4) = -1 \)**5. **\( \lim_{{x \to 1}} f(x) \) does not exist**6. **\( \lim_{{x \to 4}} f(x) = 0 \)**## b. For your graph above, at which x-values is \( f \) discontinuous and what types are they?### Explanation of the Diagrams or GraphsPlease create a graph that represents these properties:- **Discontinuity at \( x = 1 \):** Indicating the limit does not exist here, which could be shown by a jump or oscillation.- **Approach 0 as \( x \to 4 \):** Ensuring that, near \( x = 4 \), the function approaches zero, but the function value at \( x = 4 \) is \(-1\).Ensure the graph fulfills the given range and domain conditions and note where the function is discontinuous. Discuss the types of discontinuities (such as jump, infinite, or removable) in context.

a. Drawone graph of the following Properties: function t Satisfies all pe OE of Idemain 2) of f is all reals of f ís all seals s5 2(ange of f is all reals 55 3) FG5=2 4) f(4)= -| 5) lim f does exist %3D not

a. Drawone graph of the following Properties: function t Satisfies all pe OE of Idemain 2) of f is all reals of f ís all seals s5 2(ange of f is all reals 55 3) FG5=2 4) f(4)= -| 5) lim f does exist %3D not

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Soalan / Question 4 Fungsi f dan g adalah seperti berikut: The functions f and g are defined by: f(x) = x² + 3 for x > 0, 1 for x> g(x) = 2x + 1 a) Cari ungkapan bagi fg(x). Find an expression for f g(x). b) Cari ungkapan bagi (fg)-(x) dan nyatakan domain bagi (fg)-1(x). Find and expression for (f g)-1(x) and state the domain of (f g)-'(x). c) Selesaikan persamaan fg(x) – 3 = gf(x). Solve the equation f g(x) – 3 = gf (x).
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