Question

If f : A ---> B, g : B ---> C such that f(x) = log(1+x), g(x) = e^x then compute (g o f) (x) is
1. x
2. 1
3. 1 + x
4. 1 - x

Answer 1

Correct Answer - Option 3 : 1 + x

Concept:

• If f: A → B and g: B → C are functions then g o f (x) = g( f (x)) is a function from A to C.
• If g: A → B and f: B → C are functions then f o g (x) = f( g (x))

Calculation:

g o f : A ---> C is a map such that,

(g o f) (x) = g [ f(x) ] = g [ log(1 + x) ] = g (y) = e^y

               = e^{log (1 + x)} = 1 + x

where, y = log (1 + x) or (g o f) (x) = 1 + x