How do you find the domain and range of $y = 5 \sqrt{{(- x + 3)}^{4}}$ $y= 5sqrt((-x+3)^4)$ ?

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Answer 1 · 2017-11-04T07:48:29

Donain: $(- \infty, + \infty)$ $(-oo,+oo)$ Range: $[0, + \infty)$ $[0, +oo)$

$y = 5 \sqrt{{(- x + 3)}^{4}}$ $y= 5sqrt((-x+3)^4)$

$= 5 \times {(- x + 3)}^{\frac{4}{2}} = 5 {(- x + 3)}^{2}$ $= 5xx (-x+3)^(4/2) = 5(-x+3)^2$

$y$ $y$ is defined $forall x in RR$

Hence, the domain of $y$ is: $(-oo,+oo)$

$y_min = y(3) = 0$

$y$ has no finite uper bound.

Hence, the range of $y$ is: $[0, +oo)$

As can be deduced from the graph of $y$ below.

graph{5sqrt((-x+3)^4) [-2.27, 7.593, -0.676, 4.254]}

How do you find the domain and range of y= 5sqrt((-x+3)^4)y=5√(−x+3)4y= 5sqrt((-x+3)^4)?