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?
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2026-03-28 09:44:02.1774691042
Combination of functions and coordinate geometry points
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$$y=f(g(x))=\sqrt{g(x)}=\sqrt{7x+b}$$
Now plug in $x=4,y=6$ $$6=\sqrt{7 \times4 + b}$$