If the domain of f(x) is {-1, 0 5, 7} what is the range of f-1(x)

Question

I need help on this question for a test

Answer 1

f^-1(x) is the inverse function of f(x)

If, for example, f(x) = 2x, then f^-1(x) = x/2

f(x)= y,

take y=2x, switch the x and y, to get x=2y, solve for y, to get y=x/2 + f^-1(x)

the inverse switches the x and y's. If (1,2) is a point on the graph of f(x), then (2,1) is a point on the graph of f^-1(x)

x and y's are switched, including their range and domain. domain for x is the range for y, and the domain for y is the range for x

so if domain for f(x) is (-1,0,5,7) then

the range for f^-1(x) is (-1,0,5,7)

Answer 2

The range of an inverse function is the domain of the original function. The domain of the inverse function is the range of the original function.