Question: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? A. 8 B. 8 C. 25 D. 26 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.
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