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vesna_86 [32]
3 years ago
13

Given the function: f(x) = x2 – 2x How can you restrict the domain so that f(x) has an inverse? What is the equation of the inve

rse function? x ≥ 0; f Superscript negative 1 Baseline (x) = 1 + StartRoot x + 1 EndRoot x ≥ 1; f Superscript negative 1 Baseline (x) = 1 + StartRoot x + 1 EndRoot x ≥ 0; f Superscript negative 1 Baseline (x) = 1 minus StartRoot x + 1 EndRoot x ≥ 1; f Superscript negative 1 Baseline (x) = 1 minus StartRoot x + 1 EndRoot
Mathematics
2 answers:
Rina8888 [55]3 years ago
8 0

9514 1404 393

Answer:

  (b)  x ≥ 1; f⁻¹(x) = 1+√(x+1)

Step-by-step explanation:

We can find the inverse function by solving for y:

  x = f(y)

  x = y² -2y

  x +1 = y² -2y +1

  x +1 = (y -1)²

  √(x +1) = y -1

  1 +√(x +1) = y

So, the inverse function is ...

  f^{-1}(x)=1+\sqrt{x+1}

For this, the root will be non-negative, so the minimum value of this function is 1. That is, the minimum value of x for which the original function has this as an inverse is 1.

The domain restriction is x ≥ 1.

The inverse function is f⁻¹(x) = 1+√(x+1)

matrenka [14]3 years ago
4 0

Answer:

D x > 2; f Superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot

Step-by-step explanation:

Apply this method when doing problems similar to this one.

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