Question

Given the functions f(x) = 2x -1 and g(x) =

2-x, find; (25 pts)
a) f(x) + g(x) b) f(x) – g(x)
- f(-5) d) f(x).g(x) e) f(g(x))
c) g(-5)

Answer 1

Please check the explanation.

Explanation:

Given

• f(x) = 2x - 1

• g(x) = 2 - x

a)

f(x) + g(x) = (2x - 1) + (2 - x)

= 2x -1 + 2 - x

= x + 1

b)

f(x) - g(x) = (2x - 1) - (2 - x)

= 2x - 1 - 2 + x

= 3x - 3

c)

g(-5) - f(-5)

Putting x = -5 in g(x) = 2 - x

g(x) = 2 - x

g(-5) = 2 - (-5) = 2+5 = 7

Putting x = -5 in f(x) = 2x - 1

f(x) = 2x - 1

f(-5) = 2(-5) - 1

= -10 - 1

= -11

Thus,

g(-5) - f(-5) = 7 - (-11) = 7+11 = 18

d)

f(x).g(x) = (2x - 1) (2 - x) = -2x² + 5x - 2

e)

f(g(x)) = f(2-x)

= 2(2-x)-1

= 4-2x-1

= 3-2x