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Consider the functions f(x) = sqrt(x) and g(x) = 7x + b. In the standard (x,y) coordinate plane, y = f(g(x)) passes through (4,6). What is the value of b?
E. 4 - 7. sqrt(6)
Solution: (Yes we do have one)
For nested functions like f(g(x)), we must work from inside out. So we start with the function g(x) as the input value for function f(x).
Given: g(x) = 7x + b, and f(x) = sqrt(x).
So, we get, f(g(x)) = sqrt(7x + b).
We are also given that y = f(g(x)) function passes through coordinates (4,6), so let us use the value at this coordinate in the above function. Here x = 4, and y = 6. We get:
6 = sqrt(7 x 4 + b)
We can square both sides to eliminate the square root. We get:
36 = 28 + b
Or, 36 - 28 =
Or, b = 8
So the answer is A.