How do you graph $f (x) = 2 \sqrt{x}$ $f(x) = 2sqrtx$ ?

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How do you graph $f (x) = 2 \sqrt{x}$ $f(x) = 2sqrtx$ ?

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Answer 1 · 2017-11-10T02:25:32

See below

Explanation:

$f (x) = 2 \sqrt{x}$ $f(x) = 2sqrtx$

If we are confined to the real numbers, $f (x)$ $f(x)$ is only defined for positive values of $x$ $x$ and the value $0$ $0$ .

This is because the square root of a negative number is complex.

Hence, $f (x)$ $f(x)$ cannot be plotted on the real $x y -$ $xy-$ plane for $x < 0$ $x<0$ .

Also interesting in this area. When we plot $f (x)$ $f(x)$ we use the so called 'Principal Square Root' which is only the positive values of $f (x)$ $f(x)$ although:

$\sqrt{{[f (x)]}^{2}} = \pm 2 \sqrt{x}$ $sqrt([f(x)]^2) = +-2 sqrtx$

This ensures the mapping $f (x) \leftrightarrow x$ $f(x) harr x$ is one-to-one so that $f (x)$ $f(x)$ is a true function of $x$ $x$ .

The graph of $f (x)$ $f(x)$ is shown below.

graph{2sqrtx [-14.12, 14.36, -6.76, 7.48]}

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How do you graph $f (x) = 2 \sqrt{x}$ $f(x) = 2sqrtx$ ?

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