In Exercises 75–80, find the domain of each logarithmic function....

Question

In Exercises 75–80, find the domain of each logarithmic function. f(x) = log (2 - x)

Accepted Answer

Welcome back. I am so glad you're here. We are given this function F of X equals the log of eight minus x. And we are asked to find the domain. Well, whenever we have a log we do have a domain restriction. What we're taking the log of. So in this case eight minus X must be greater than zero. So let's find out what X values make this true. Let's solve for X. So we'll subtract eight from both sides and that will give us negative X is greater than negative. Eight Will divide both sides by -1. And we need to remember to flip the sign there. So because we're dividing by a negative so now it will be X is less than and negative eight divided by negative one is positive eight. So we can think of this on a number line for our X axis and we have got an eight as a boundary. It cannot be eight. So express that with an open circle and X has to be less than eight. So it's going to the left toward negative infinity. How do we express this? An interval notation? Well, starting with negative infinity, that's going to be a parentheses negative infinity comma going all the way up to eight. But because it will never be able to touch eight, we're going to close eight with a parentheses. We look at our answer choices and this matches with answer choice C Well done. We'll catch you on the next one

In Exercises 75–80, find the domain of each logarithmic function. f(x) = log (2 - x)

Key Concepts

Logarithmic Functions

Domain of a Function

Inequalities

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