If f(x) and r^(x) are inverse functions of eachother and f(x)=2x+5 what is f-1(8)?

recall that for inverse functions, the range of the original is the domain of the inverse and othe other way around.

so f⁻¹(8) is f⁻¹(x) but making x = 8, so the domain value in this case for the inverse is 8, and that's going to give us something, but let's nevermind that.

since the domain value is 8 for the inverse, that means, the same 8, is a range for the original f(x).

meaning, "some value of x" on the original, gives us a range of 8, then let's use that 8 in the original, BUT not on "x", but on "y", or f(x).

so notice how the values swap places for the inverses, one's domain, is the other's range.