Given $f (x) = \sqrt{x}$ $f(x)=sqrtx$ and $g (x) = x - 1$ $g(x)=x-1$ , how do you determine the domain and range of $y = f (g (x))$ $y=f(g(x))$ ?

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Given $f (x) = \sqrt{x}$ $f(x)=sqrtx$ and $g (x) = x - 1$ $g(x)=x-1$ , how do you determine the domain and range of $y = f (g (x))$ $y=f(g(x))$ ?

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Answer 1 · 2017-06-20T11:43:26

Domain : $x \geq 1$ $x>=1$ . In interval notation $[1, \infty)$ $[1,oo)$
Range: $y \geq 0$ $y>=0$ . In interval notation $[0, \infty)$ $[0,oo)$

Explanation:

$f (x) = \sqrt{x}; g (x) = x - 1; y = f (g (x)) = ?$ $f(x)=sqrtx ; g(x)=x-1 ; y=f(g(x))= ?$

Here Inside function is $g (x) = x - 1$ $g(x)=x-1$ . Domain of inside function is any real number $x in RR$ , Range: $g(x) in RR$

$y=f(g(x)) = f(x-1) = sqrt(x-1)$ . Domain: under root should be $>=0 :. x-1>=0 or x>=1$ .

Domain : $x>=1$ .In interval notation $[1,oo)$

Range: $y>=0$ In interval notation $[0,oo)$
graph{sqrt(x-1) [-10, 10, -5, 5]} [Ans]

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Given $f (x) = \sqrt{x}$ $f(x)=sqrtx$ and $g (x) = x - 1$ $g(x)=x-1$ , how do you determine the domain and range of $y = f (g (x))$ $y=f(g(x))$ ?

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Given f(x)=sqrtxf(x)=√xf(x)=sqrtx and g(x)=x-1g(x)=x−1g(x)=x-1, how do you determine the domain and range of y=f(g(x))y=f(g(x))y=f(g(x))?

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Explanation:

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Given $f (x) = \sqrt{x}$ $f(x)=sqrtx$ and $g (x) = x - 1$ $g(x)=x-1$ , how do you determine the domain and range of $y = f (g (x))$ $y=f(g(x))$ ?