rafalalhilfi2004 rafalalhilfi2004
  • 13-03-2022
  • Mathematics
contestada

If f(-4) for f(x)=-2x+7 is 15, then what is f^-1 (15)?

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jdoe0001 jdoe0001
  • 13-03-2022

let's recall that for a function f(x) that has an inverse function f⁻¹(x), the domain of f(x) corresponds to the range of f⁻¹(x), what the heck does that all mean?

well, it means that for any coordinate pairs (a , b) in f(x), there's a corresponding pair of (b , a) on f⁻¹(x).

we know in this case that f(-4) = 15, or namely that f(x) has a pair of (-4 , 15), well, that means that f⁻¹(x) has a swapped pair of (15 , -4).

the above means that f⁻¹(15) = -4.

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