SOLUTION: I have three simple questions about the domain and range of functions: 1). +sqrt(x-1) 2). (10^x)+3 3). Log base 2(x-3) Thank you!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I have three simple questions about the domain and range of functions: 1). +sqrt(x-1) 2). (10^x)+3 3). Log base 2(x-3) Thank you!      Log On


   

Question 722950: I have three simple questions about the domain and range of functions:
1). +sqrt(x-1)
2). (10^x)+3
3). Log base 2(x-3)
Thank you!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
  1. sqrt%28x-1%29
    • Domain: "x" is in the radicand of an even-numbered root (square root is a "2nd root"). The radicand of an even-numbered root must not be negative. (IOW: It must be greater than or equal to zero.) So:
      x-1+%3E=+0
      or
      x+%3E=+1
      This is the domain.
    • Range: The expression as a whole is a square root. This cannot be negative, either. So the range is zero and all positive numbers.
  2. %2810%5Ex%29%2B3
    • Domain: "x" is in an exponent. Exponents can be any number. So the domain is all real numbers.
    • Range. A power of 10 can never be zero or negative. (IOW: A power of 10 must be positive.) It can be any positive number. So 10%5Ex+%3E+0. If we add three to each side we get: 10%5Ex+%2B+3+%3E+3. On the left side we have the expression we started with. So this inequality tells us that the range is all numbers greater than 3.
  3. log%282%2C+%28x-3%29%29
    • "x" is in the argument of a logarithm. Arguments of logarithms must be positive. So
      x - 3 > 0
      or
      x > 3
      This is the domain.
    • Range: The expression as a whole is a logarithm. The value of a logarithm can be any real number so the range is all real numbers.