What is the domain and range of $y = ln (6 - x) + 2$ $y= ln(6-x) +2$ ?

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Answer 1 · 2017-06-08T20:55:33

Domain $x \in (- \infty, 6)$ $x in(-oo,6)$
Range= $y \in (- \infty, (ln 6) + 2)$ $yin(-oo,(ln 6) +2)$

TO find the domain we take the values of $X$ $X$ for which the function is defined.
for this the input of log cannot be negative or zero so

$6 - x > 0$ $6-x>0$
$x < 6$ $x<6$

hence Domain of definition extends from
$x \in (- \infty, 6)$ $x in(-oo,6)$

Now for range we see the graph graph{ln x [-10, 10, -5, 5]}

so putting $x = 6$ $x=6$ in graph of $y = ln x$ $y=lnx$

we get $ln 6$ $ln6$

$y \in (- \infty, ln 6 + 2$ $yin(-oo,ln6 +2$
$y \in (- \infty, (ln 6) + 2)$ $yin(-oo,(ln 6) +2)$

What is the domain and range of y=ln(6−x)+2y= ln(6-x) +2?