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yan [13]
3 years ago
12

Given the functions, fx) = x^2-4 and g(x) = x+ 2, perform the indicated operation. When applicable, state the domain

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
6 0

ANSWER

f(g(x)) =  {x}^{2}  + 2x

EXPLANATION

The given functions are:

f(x) =  {x}^{2}  - 4

and

g(x) =  x + 2

We want to find

f(g(x)) = f(x + 2)

We substitute x+2 wherever we see x in f(x).This implies that;

f(g(x)) = (x + 2)^{2}  - 4

We can rewrite the perfect square term as

f(g(x)) = (x + 2)(x + 2)- 4

We expand to get:

f(g(x)) =  {x}^{2}  + 2x + 4- 4

This simplifies to

f(g(x)) =  {x}^{2}  + 2x

This is a polynomial function. The domain of this function is the values of x for which the function is defined. Since polynomials are defined for all real values, the domain is all real numbers.

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