False. The statement suggests that the y-intercept of a function is also an x-intercept of its inverse, but this isn’t necessarily true.
To understand why, recall that the y-intercept of a function f(x) is the point where the graph intersects the y-axis, which occurs when x = 0. So, the y-intercept has coordinates (0, f(0)). Meanwhile, an x-intercept is the point where the function equals zero, meaning f(x) = 0 for some x.
For the inverse function f-1(x) to exist, the original function f(x) must pass the horizontal line test, meaning it is one-to-one and has a unique output for each input. However, the relationship between the y-intercept of f and the x-intercept of f-1 is not one where the y-intercept of f can be assumed to be an x-intercept of f(1). The points may not satisfy this condition at all.
In conclusion, just because a function has a y-intercept does not imply that this point will be an x-intercept for its inverse, making the statement false.