If f(x) = sqrtx and g(x) = sqrt3-x, find g circ f and f circ g. | Mathematics I 2074

Mathematics I20745 marksNumerical: function compositionCombination of functions

If $f(x) = \sqrt{x}$ and $g(x) = \sqrt{3-x}$ , find $g \circ f$ and $f \circ g$ . [5]

If $f(x) = \sqrt{x}$ and $g(x) = \sqrt{3-x}$, find $g \circ f$ and $f \circ g$. [5]

$f(x) = \sqrt{x}$ - $g(x) = \sqrt{3-x}$ Required: $g\circ f$ and $f\circ g$ (with domains). All data present and readable. --- $(g\circ f)(x) = g(f(x)) = g(\sqrt{x}) = \sqrt{3 - \sqrt{x}}$ Domain: For $f(x)=\sqrt{x}$ : need $x \geq 0$ . For $\sqrt{3-\sqrt{x}}$ : need $$3 - \sqrt{x} \geq 0 \impli...

$f(x) = \sqrt{x}$ - $g(x) = \sqrt{3-x}$ Required: $g\circ f$ and $f\circ g$ (with domains). All data present and readable. --- $$(g\circ f)(x) = g(f(x)) = g(\sqrt{x}) = \sqrt{3 - \sqrt{x}}$$ Domain: For $f(x)=\sqrt{x}$: need $x \geq 0$. For $\sqrt{3-\sqrt{x}}$: need $$3 - \sqrt{x} \geq 0 \impli...