Question If f(x) = sqrtx and g(x) = sqrt3-x, then find f circ g and it | Mathematics I 2078

Mathematics I207810 marksNumerical: Function composition and cost functionCombination of functions

Question

If $f(x) = \sqrt{x}$ and $g(x) = \sqrt{3-x}$ , then find $f \circ g$ and its domain and range.

A rectangular storage container with an open top has a volume of $20 \text{ m}^3$ . The length of its base is twice its width. Material for the base costs Rs 10 per square meter; material for the sides costs Rs 4 per square meter. Express the cost of materials as a function of the width of the base.

[5+5]

Question

If $f(x) = \sqrt{x}$ and $g(x) = \sqrt{3-x}$, then find $f \circ g$ and its domain and range.

A rectangular storage container with an open top has a volume of $20 \text{ m}^3$. The length of its base is twice its width. Material for the base costs Rs 10 per square meter; material for the sides costs Rs 4 per square meter. Express the cost of materials as a function of the width of the base.

[5+5]

(a) Finding fog, its Domain and Range $f(x) = \sqrt{x}, \qquad g(x) = \sqrt{3-x}$ $fog(x) = f(g(x)) = f\left(\sqrt{3-x}\right) = \sqrt{\sqrt{3-x}} = (3-x)^{1/4}$ $\boxed{fog(x) = (3-x)^{1/4}}$ Domain analysis via composition: - $g(x) = \sqrt{3-x}$ requires

(a) Finding fog, its Domain and Range $$f(x) = \sqrt{x}, \qquad g(x) = \sqrt{3-x}$$ $$fog(x) = f(g(x)) = f\left(\sqrt{3-x}\right) = \sqrt{\sqrt{3-x}} = (3-x)^{1/4}$$ $$\boxed{fog(x) = (3-x)^{1/4}}$$ Domain analysis via composition: - $g(x) = \sqrt{3-x}$ requires

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Question If f(x) = sqrtx and g(x) = sqrt3-x, then find f circ g and its domain and range. A rectangular storage container with an open top has a volume of 20 text m3. The length of its base is twice its width. Material for the base costs Rs 10 per square meter; material for the sides costs Rs 4 per