Question

Let f, g: R → R be defined respectively, and f(x) = x² - 12x + 32, g(x) = x -3. Find f o g (1).
1. 30
2. 40
3. 50
4. 60

Answer 1

Correct Answer - Option 4 : 60

CONCEPT:

Let f: A → B and g: B → C be two functions. Then, the composition of f and g, denoted by g o f, is defined as the function g o f: A → C given by g o f (x) = g (f (x)), ∀ x ∈ A.

CALCULATIONS:

Given functions are f(x) = x ² - 12x + 32, g(x) = x -3.

f o g means g(x) function is in f(x) function.

This means put x = x -3 in function f(x).

f[g(x)] = (x - 3) ² - 12(x -3) + 32

f[g(x)] = x² – 18x + 77

now we have to find f o g (1).

∴ f [g (1)] = 1² – 18+ 77 = 60