Question

Find an equation for the inverse for each of the following.

Answer 1

Answer:

• To solve these first swap x and y, solve for y and name it inverse function

3. y = -8x + 2

• x = -8y + 2
• 8y = -x + 2
• y = -x/8 + 2/8
• y = -(18)x + 1/4

f⁻¹(x) = -(18)x + 1/4

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4. y = (2/3)x - 5

• x = (2/3)y - 5
• (2/3)y = x + 5
• y = (3/2)x + (3/2)5
• y = 1.5x + 7.5

f⁻¹(x) = 1.5x + 7.5

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5. f(x) = 2x² - 6

• x = 2y² - 6
• 2y² = x + 6
• y² = 1/2x + 3
• y = $\sqrt{1/2x + 3}$

f⁻¹(x) = $\sqrt{1/2x + 3}$

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6. y = (x - 3)²

• x = (y - 3)²
• $\sqrt{x}$ = y - 3
• y = 3 + $\sqrt{x}$

f⁻¹(x) = 3 +  $\sqrt{x}$