Answer:
f(x) does not have an inverse function, because its graph fails the horizontal line test. ⇒ A
Step-by-step explanation:
The vertical line test is used to show that the graph represents a
function or not
- If the vertical line crosses the graph in more than one point, then the graph does not represent a function
- If the vertical line crosses the graph in only one point in different positions, then the graph represents a function
The horizontal line test is used to show that the function has an
inverse or not
- If the horizontal line crosses the graph of a function in more than one point, then the function has no inverse
- If the horizontal line crosses the graph of a function in only one point in different positions, then the function has an inverse
Let us look at the given graph
→ The graph represents a parabola, which represents the function f(x)
∵ Any horizontal line drawn will cross the graph in more than one point
∴ f(x) has no inverse
∴ f(x) does not have an inverse function, because its graph fails the
horizontal line test.
