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