What is the domain and range of $f (x) = ln (- x + 5) + 8$ $f(x) = ln(-x + 5) + 8$ ?

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Answer 1 · 2018-04-29T13:27:21

The domain is $x \in (- \infty, 5)$ $x in (-oo, 5)$ . The range is $y \in (- \infty, + \infty)$ $y in (-oo, +oo)$

Let $y = ln (- x + 5) + 8$ $y=ln(-x+5)+8$

For the natural log,

$- x + 5 > 0$ $-x+5>0$

Therefore,

$x < 5$ $x<5$

The domain is $x \in (- \infty, 5)$ $x in (-oo, 5)$

$lim_(x->-oo)y=+oo$

$lim_(x->5)y=-oo$

The range is $y in (-oo, +oo)$

graph{ln(5-x)+8 [-47.05, 17.92, -10.28, 22.2]}

What is the domain and range of f(x) = ln(-x + 5) + 8f(x)=ln(−x+5)+8f(x) = ln(-x + 5) + 8?