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Chapter 5: Q 112 (page 299)

Suppose that F(x)=log2(x+1)-3.

(a) What is the domain of F?

(b) What is F(7)? What point is on the graph of F?

(c) If F(x)=-1, what is x? What point is on the graph of F?

(d) What is the zero of F?

Short Answer

Expert verified

(a) The domain of F is (-1,鈭�).

(b) The value of F(7)=0.

(c) The value of x is 3 when F(x)=-1.

(d) The zero of F(x) is 7.

Step by step solution

01

Step 1. Given information.

The following function F(x)=鈥�log2x+1-3is given.

02

Step 2. The domain and the roots.

(a) Here, x+1=0

x>-1 .

So, the domain is (-1,0).

(b)

G(x)=log2(x+1)-3G(7)=log2(7+1)-3=0(c)log2(x+1)-3=3x+1=20x=-1(d)log2(x+1)-3=0log2(x+1)=3x+1=23x=7

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