SOLUTION: Suppose that F(x) =log 2 (x+1)-3 a) what s the domain of F? what is F(7)? what point is on the graph of F? b) if F(x)=-1, what is x? what point s on the graph of F? c)What is t

Question 574198: Suppose that F(x) =log 2 (x+1)-3
a) what s the domain of F?
what is F(7)? what point is on the graph of F?
b) if F(x)=-1, what is x? what point s on the graph of F?
c)What is the zero of F
please explain me or show me how should I do b, and c, i do know how to do a.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

b) F(x) = -1
Substitute the given value for F(x):

Now solve for x.

To solve for x in an equation like this we usually start by transforming the equation into one of the following forms:
log(expression) = other_expression
or
log(expression) = log(other_expression)

Since your equation has only a single log in it, we will aim for the first form. All we have to do to add three to each side:

With the equation in the first form, then next step is to rewrite the equation in exponential form. In general, is equivalent to . Using this pattern on your equation we get:

which simplifies to:
4 = x + 1

With the logarithm now gone the equation is simple to solve, Just subtract 1 from each side:
3 = x

When solving equations like

it is important, not optional, to check your answer! You have to ensure that all arguments (and bases) remain valid (i.e. positive). Checking x = 3:

We can quickly see that the only log's argument is 4. And its base is 2. These are both valid/allowable numbers so the required part of the check is complete.

So F(3) = -1 which means the point (3, -1) is a point on the graph of F(x).

c) Find the zeros. This just means find the x value or values where the function's value is zero. IOW: Find all x's such that F(x) = 0. Solve this just like part b (using 0, instead of -1 of course).

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