Q7 of 118 Page 3

The function f is defined by . Draw the graph of f(x).

Given

When x < 0, we have f(x) = 1 – x

f(–4) = 1 – (–4) = 1 + 4 = 5

f(–3) = 1 – (–3) = 1 + 3 = 4

f(–2) = 1 – (–2) = 1 + 2 = 3

f(–1) = 1 – (–1) = 1 + 1 = 2

When x = 0, we have f(x) = f(0) = 1

When x > 0, we have f(x) = 1 + x

f(1) = 1 + 1 = 2

f(2) = 1 + 2 = 3

f(3) = 1 + 3 = 4

f(4) = 1 + 4 = 5

Plotting these points on a graph sheet, we get

If f(x) = log_e(1 – x) and g(x) = [x], then determine each of the following functions:

i. f + g

ii. fg

iii.

iv.

Also, find (f + g)(–1), (fg)(0), and .

If f, g, h are real functions defined by, and h(x) = 2x² – 3, then find the values of (2f + g – h)(1) and (2f + g – h)(0).

Let f, g : R → R be defined, respectively by f(x) = x + 1 and g(x) = 2x – 3. Find f + g, f – g and.

Find the domain in each case.

Let f : [0, ∞) → R and g : R → R be defined by and g(x) = x. Find f + g, f – g, fg and