On this one which you answered for me before, could you do the step by steps so I can learn it better?
Evaluate the function g(x)= √x^2+1 at each specified value of the independent variable, and simplify.
a). g(-1)
b. g(3)
c. g(3x)
thanks, Maria
g(x)= √(x^2+1)
The x is just a place holder. You can replace it with whatever value you want, as long as every x is replaced
g(-1) = √((-1)^2+1) = √(1+1) = √2
g(3) = √(3^2+1) = √(9+1) = √10
g(3x) = √((3x)^2 +1) = √(9x^2 + 1)
g(2x-3) = √((2x-3)^2 + 1) = √(4x^2-6x+9 + 1) = √(4x^2-6x+10)
and so on
love you!
Certainly, Maria! I'd be happy to explain the step-by-step process for evaluating the function g(x) = √(x^2 + 1) at the specified values of the independent variable.
a) To evaluate g(-1), we substitute the value -1 in place of x in the function g(x).
Step 1: Replace every x in the function with -1:
g(-1) = √((-1)^2 + 1)
Step 2: Simplify the expression inside the square root:
g(-1) = √(1 + 1)
g(-1) = √2
So, g(-1) = √2, which is the simplified answer.
b) To evaluate g(3), we substitute the value 3 in place of x in the function g(x).
Step 1: Replace every x in the function with 3:
g(3) = √(3^2 + 1)
Step 2: Simplify the expression inside the square root:
g(3) = √(9 + 1)
g(3) = √10
So, g(3) = √10, which is the simplified answer.
c) To evaluate g(3x), we substitute the expression 3x in place of x in the function g(x).
Step 1: Replace every x in the function with 3x:
g(3x) = √((3x)^2 + 1)
Step 2: Simplify the expression inside the square root:
g(3x) = √(9x^2 + 1)
So, g(3x) = √(9x^2 + 1), which is the simplified answer.
These are the step-by-step instructions to evaluate the function g(x)= √(x^2 + 1) at each specified value of the independent variable. I hope this helps you understand the process better! If you have any further questions, feel free to ask.