Let f (x) = e^x and G (x) = x+6. What are the domain and range of g (f (x)) ?

Domain and Range of g (f (x)) are 'All real numbers' and y>6 respectively

Step-by-step explanation:

We have the functions, f (x) = eˣ and g (x) = x+6

So, their composition will be g (f (x)).

Then, g (f (x)) = g (eˣ) = eˣ+6

Thus, g (f (x)) = eˣ+6.

Since the domain and range of f (x) = eˣ are all real numbers and positive real numbers respectively.

Moreover, the function g (f (x)) = eˣ+6 is the function f (x) translated up by 6 units.

Hence, the domain and range of g (f (x)) are 'All real numbers' and y>6 respectively.