Question

 f(x) = 2x + 9

g(x) = 3x + 8

Find f[g(x)] – g[f(x)].

1. 10
2. 15
3. -10
4. -15

Answer 1

Correct Answer - Option 3 : -10

Given:

f(x) = 2x + 9

g(x) = 3x + 8

Calculations:

f[g(x)] = 2(3x + 8) + 9

⇒ f[g(x)] = 2(3x + 8) + 9

⇒ f[g(x)] = 6x + 16 + 9 = 6x + 25

g[f(x)] = 3(2x + 9) + 8

⇒ g[f(x)] = 6x + 27 + 8 = 6x + 35

f[g(x)] – g[f(x)]

6x + 25 – (6x + 35)

⇒ 6x + 25 – 6x – 35 = -10

∴ value of f[g(x)] – g[f(x)] is -10