فرمولی برای \(f \circ g \circ h\) بنویسید.





$$
f(x) = \sqrt{x+1}\\
g(x) = \frac{1}{x+4}\\
h(x) = \frac{1}{x}
$$

پاسخ

$$
(f \circ g \circ h)(x) = f(g(h(x)) = f (g(\frac{1}{x})) = f(\frac{1}{\frac{1}{x}+4}) \\
= f(\frac{1}{\frac{1+4x}{x}}) = f(\frac{x}{1+4x})\\
= \sqrt{\frac{x}{1+4x}+1} = \sqrt{\frac{x+1+4x}{1+4x}} = \sqrt{\frac{5x+1}{1+4x}}
$$