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poizon [28]
3 years ago
15

Functions:

Mathematics
1 answer:
vitfil [10]3 years ago
7 0

Answer:

<h3>Image 1</h3>

1. <u>x = 4 </u>

  • f(4) = (- 3*4 + 1) / 6 = -11/6

2. <u>x = -2/3</u>

  • f(-2/3) = -3*(-2/3) + 10 = 2 + 10 = 12

3. <u>x = -5</u>

  • f(-5) = \sqrt{-(-5)/20} = \sqrt{5/20} = \sqrt{1/4} = 1/2
<h3>Image 2</h3>
  • <em>To work out the inverse, substitute f(x) with x and x with y, then solve for y. The new function is the inverse of the given.</em>

1. <u>f(x) = 5x + 3</u>

  • x = 5y + 3 ⇒ 5y = x - 3 ⇒ y = (x - 3)/5
  • f⁻¹(x) =  (x - 3)/5

2.<u> f(x) = 4/5x</u>

  • x = 4/5y ⇒ y = 5/4x
  • f⁻¹(x) = 5/4x

3. <u>f(x) = (2x + 7)/4</u>

  • x = (2y + 7)/4 ⇒ 2y + 7 = 4x ⇒ 2y = 4x - 7 ⇒ y = 2x - 3.5
  • f⁻¹(x) = 2x - 3.5

4.<u> f(x) = (2x + 7) /(x + 3) </u>= 2 + 1/(x + 3)

  • x = 2 +  1/(y + 3) ⇒ x - 2 = 1/(y + 3) ⇒ y + 3 = 1/(x - 2) ⇒ y = (1 - 3x + 6)/(x - 2) ⇒ y = (7 - 3x)/(x - 2)
  • f⁻¹(x) =  (7 - 3x)/(x - 2)

5.<u> f(x) = </u>\sqrt{x - 4}<u> </u>

  • x = \sqrt{y - 4} ⇒ x² = y - 4 ⇒ y = x² + 4
  • f⁻¹(x) = x² + 4
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