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

Jun 8, 2017

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

#### Explanation:

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

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

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

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

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

we get $\ln 6$

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