let fx x2 4x 2 and gx 2x 1 Find ga 4 f3 f3 f g0 fg2 t

let f(x) = x^2 + 4x - 2 and g(x) = 2x + 1. Find: g(a + 4) f(-3) (f(-3) (f + g)(0) (fg)(-2) the domain of f/g

Solution

Given that

f(x) = x² + 4x - 2 , g(x) = 2x + 1

5 ) g(a + 4) = 2(a + 4) + 1 [ Since , g(x) = 2x + 1 ]

= 2a + 8 + 1

g(a + 4) = 2a + 9

6 ) f(x) = x² + 4x - 2   

  f(-3) = (-3)² + 4.(-3) - 2

= 9 - 12 - 2

f(-3) = -5

7 ) (f + g)(0) = f(0) + g(0)

  f(x) = x² + 4x - 2

  f(0) = (0)² + 4.(0) - 2

f(0) = -2

g(x) = 2x + 1

g(0) = 2(0) + 1

g(0) = 1

Hence ,

  (f + g)(0) = f(0) + g(0)

  (f + g)(0) = -2 + 1

(f + g)(0) = -1

8 ) (fg)(-2) = f(-2).g(-2)

f(x) = x² + 4x - 2

  f(0) = (-2)² + 4.(-2) - 2

f(0) = 4 - 8 - 2

    f(0) = -6

g(x) = 2x + 1

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

g(-2) = -3

Hence ,

  (fg)(-2) = f(-2).g(-2)

= (-6).(-3)

  (fg)(-2) = 18