To show that f(x) = sqrt(x-2) is one-to-one, we need to prove that if f(a) = f(b), then a = b. Let's assume that f(a) = f(b), which gives us sqrt(a-2) = sqrt(b-2). Squaring both sides of the equation, we get a-2 = b-2, and therefore a = b. This shows that f(x) = sqrt(x-2) is one-to-one.
To show that the function f(x) = sqrt(x-2) is one-to-one, we need to prove that if f(a) = f(b), then a = b. Let's assume that f(a) = f(b), which gives us sqrt(a-2) = sqrt(b-2). Squaring both sides of the equation, we get a-2 = b-2, and therefore a = b. This shows that f(x) = sqrt(x-2) is one-to-one.
To find f(21), we substitute x = 21 into the function. f(21) = sqrt(21-2) = sqrt(19).
For f(21), the domain is the set of all real numbers greater than or equal to 2, and the range is the set of all real numbers greater than or equal to 0. So, the domain and range of f(21) are [2, ∞) and [0, ∞) respectively.
To calculate sqrt(21-2) using the formula from part (c), we substitute x = 21 into the function. sqrt(21-2) = sqrt(19). This agrees with the result from part (b).
To sketch the graphs of f(x) = sqrt(x-2) and f(21), we can plot the points on a coordinate plane using a suitable scale and connect them to form the graphs.