Let f(g(x)) = 3x + 3 and f(x) = x + 6/ If g(x) = ax + b, compute a + b

Answer 1

To find a + b, we need to determine the values of a and b such that f(g(x)) = 3x + 3.

First, substitute g(x) into the expression for f(x):
f(g(x)) = f(ax + b) = (ax + b) + 6

Now, set this expression equal to 3x + 3 and solve for a and b:
(ax + b) + 6 = 3x + 3
ax + b = 3x - 3

The coefficient of x on the left side must be 3 for the equation to be equal to 3x. This means that a = 3.

Substituting a = 3 into the equation, we have:
3x + b = 3x - 3

To make the constant term on the left side equal to -3, b must be -3.

Therefore, a = 3 and b = -3.

Finally, compute a + b:
a + b = 3 + (-3) = 0