Question

For f(x) = 3x² + 5 and g(x)=7x-2,
a. Verify: g(x + 2) + g(x) + g(2).

Answer 1

After substituting the required values into the function g(x) = 7x - 2, we find that g(x + 2) + g(x) + g(2) equals 14x + 22.

Step-by-step explanation:

To verify the equation g(x + 2) + g(x) + g(2), we must first calculate each of the individual terms using the given function g(x) = 7x - 2.

• For g(x + 2), we substitute (x + 2) for x in g(x):
  g(x + 2) = 7(x + 2) - 2 = 7x + 14 - 2 = 7x + 12

• For g(x), we substitute x in g(x):
  g(x) = 7x - 2

• For g(2), we substitute 2 for x in g(x):
  g(2) = 7(2) - 2 = 14 - 2 = 12

Next, we sum these terms:
g(x + 2) + g(x) + g(2) = (7x + 12) + (7x - 2) + 12

The terms will be combined to yield:
7x + 12 + 7x - 2 + 12 = 14x + 22

Therefore, after verifying, we find that g(x + 2) + g(x) + g(2) = 14x + 22, which is the sum of all individual values of g for the respective arguments.