Questions: The graph of (f) is given. (i) (a) Why is (f) one-to-one? (f) is one-to-one because it passes the Horizontal Line Test (b) What are the domain and range of (f^-1)? (Enter your answers in interval notation.) domain [ [0,4] ] range (c) What is the value of (f^-1(2))? Enter a number. (d) Estimate the value of (f^-1(1)) to the nearest tenth.

Solution Steps

• The function \( f \) is one-to-one because it passes the Horizontal Line Test. This means that any horizontal line drawn through the graph intersects it at most once.

• The domain of \( f^{-1} \) is the range of \( f \), which is \([-4, 2]\).
• The range of \( f^{-1} \) is the domain of \( f \), which is \([0, 4]\).

• To find \( f^{-1}(2) \), we need to determine the x-value for which \( f(x) = 2 \).
• From the graph, when \( y = 2 \), \( x = 0 \).

Final Answer