which of the following is the domain and range of the inverse of Y equals two square root of X -6 +4
To determine the domain and range of the inverse of the given function, let's start by finding the inverse function of f(x) = 2√(x) - 6 + 4.
Step 1: Replace f(x) with y:
y = 2√(x) - 6 + 4
Step 2: Swap x and y:
x = 2√(y) - 6 + 4
Step 3: Solve for y:
x - 4 = 2√(y) - 6
2 = 2√(y)
1 = √(y)
1 = y
So, the inverse of the given function is f^(-1)(x) = 1.
Now, let's determine the domain and range of the inverse function.
Domain:
The domain of the inverse function is the set of all possible values that x can take. Since the inverse of f(x) = 2√(x) - 6 + 4 is f^(-1)(x) = 1, the domain is all real numbers.
Domain: (-∞, +∞)
Range:
The range of the inverse function is the set of all possible values that y can take. Since the inverse function is a constant function f^(-1)(x) = 1, the range is a single value.
Range: {1}