To solve for the value of x such that f(g(x)) = 0, we first need to find g(x) and then substitute it into f(x).
Given:
- f(x) = 16x + 30
- g(x) = 14x + 6
Now, we can find f(g(x)). First, we need to substitute g(x) into f(x):
f(g(x)) = f(14x + 6)
Now, replace x in f(x):
f(14x + 6) = 16(14x + 6) + 30
Distributing the 16:
f(14x + 6) = 224x + 96 + 30
Combining like terms:
f(14x + 6) = 224x + 126
Now set f(g(x)) equal to 0:
224x + 126 = 0
To isolate x, first subtract 126 from both sides:
224x = -126
Now divide both sides by 224:
x = -126 / 224
Simplifying this fraction gives:
x = -63 / 112
Thus, the value of x for which f(g(x)) = 0 is -63 / 112.