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2 years ago

The table below shows some inputs and outputs of the invertible function with domain all real numbers.

Mathematics

1 answer:

gizmo_the_mogwai [7]2 years ago

6 0

Answer:

f⁻¹(-2) = 3 and f⁻¹(1) = 0.

Step-by-step explanation:

By the definition of inverse functions:

$\displaystyle \text{If } f(a) = b\text{, then } f^{-1}(b) = a$

From the table, note that f(3) = -2.

Then by definition, f⁻¹(-2) = 3.

Likewise, f(0) = 1.

Then by definition, f⁻¹(1) = 0.

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<u>SOLUTION:</u>

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$\begin{array}{l}{X=\frac{-12 \pm \sqrt{144-96}}{2}} \\\\ {X=\frac{-12 \pm \sqrt{48}}{2}} \\\\ {X=\frac{-12 \pm \sqrt{16 \times 3}}{2}} \\\\ {X=\frac{-12 \pm 4 \sqrt{3}}{2}} \\ {X=\frac{2(-6+2 \sqrt{3})}{2}, \frac{2(-6-2 \sqrt{3})}{2}} \\\\ {X=(-6+2 \sqrt{3}),(-6-2 \sqrt{3})}\end{array}$

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