evaluate the funtions at the specified values of the independent vaiable and simplify f(x)= (x+8)^1/2+2 a. f(1) b. f(x-8)
To evaluate the given function at the specified values, you need to substitute the values into the function and simplify the expression.
a. Let's evaluate f(1). Replace x with 1 in the function:
f(x) = (x + 8)^(1/2) + 2
f(1) = (1 + 8)^(1/2) + 2
Now, simplify the expression:
f(1) = 9^(1/2) + 2
The square root of 9 is 3:
f(1) = 3 + 2
f(1) = 5
Therefore, f(1) = 5.
b. Now, let's evaluate f(x - 8). Replace x with (x - 8) in the function:
f(x) = (x + 8)^(1/2) + 2
f(x - 8) = ((x - 8) + 8)^(1/2) + 2
The (x - 8) + 8 simplifies to x:
f(x - 8) = x^(1/2) + 2
Hence, f(x - 8) = x^(1/2) + 2.