Question

For each pair of functions, f and g, find f[g(x)] and g[(x)]f(x)= 2x +1g(x)= x-3​

Answer 1

To find f(g(x)), substitute g(x) into f, resulting in 2x - 5. For g(f(x)), substitute f(x) into g, resulting in 2x - 2. These are the composite functions required.

Step-by-step explanation:

To find the composition of the two functions f(g(x)), we substitute g(x) into the function f. Given f(x) = 2x + 1 and g(x) = x - 3, we replace every x in f(x) with g(x) to get:

f(g(x)) = 2(g(x)) + 1 = 2(x - 3) + 1 = 2x - 6 + 1 = 2x - 5.

Similarly, to find g(f(x)), we substitute f(x) into the function g. This results in:

g(f(x)) = f(x) - 3 = (2x + 1) - 3 = 2x + 1 - 3 = 2x - 2.