f(x) = √x
g(x) = 3x – b

If the graph of y = f(g(x)) passes through (6, 5) in the standard (x, y) coordinate plane, what is the value of b?

When you have functions nested like this, start from the middle and work outwards. So start by replacing g(x) with 3x-b:


Now note that all the f function does is take the square root of the whole argument. In other words, if f(x)=\sqrt{x}, then we know that f(3x-b)=\sqrt{3x-b}.

The question tells us that if we graph y=\sqrt{3x-b}, it passes through (6, 5). So let’s plug that point in and solve:







Let’s check our work here. If b=-7, then the graph of y=\sqrt{3x+7} should pass through (6, 5). And it does!

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