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Answer 1

Answer:

A. 8

Step-by-step explanation:

We are given the functions:

$f(x)=\sqrt{x}\\\\g(x)=7x+b$

    We are told that on a standard (x, y) coordinate plane that y = f(g(x)) passes through the point (4, 6). In order to solve for b, we need to figure out what f(g(x)) is equal to.

    As with a regular function like the two above, f(g(x)) means you are substituting x with g(x) in function f. The problem gave us the two functions, so I will demonstrate what I mean.

$f(g(x))=\sqrt{(7x+b)}$

    The problem again tells us that y = f(g(x)) goes through (4, 6). Substitute those values for their respective variables and solve for b.

$y=f(g(x))\\\\y=\sqrt{(7x+b)}\\\\6=\sqrt{(7(4)+b)}\\\\6=\sqrt{(28+b)}\\\\(6)^2=(\sqrt{(28+b)})^2\\\\36=28+b\\\\36-28=28+b-28\\\\8=b$

Therefore, the value of b is equal to 8.