Answer:
Image 1
1. x = 4
- f(4) = (- 3*4 + 1) / 6 = -11/6
2. x = -2/3
- f(-2/3) = -3*(-2/3) + 10 = 2 + 10 = 12
3. x = -5
- f(-5) = [tex]\sqrt{-(-5)/20}[/tex] = [tex]\sqrt{5/20}[/tex] = [tex]\sqrt{1/4}[/tex] = 1/2
Image 2
- 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.
1. f(x) = 5x + 3
- x = 5y + 3 ⇒ 5y = x - 3 ⇒ y = (x - 3)/5
- f⁻¹(x) = (x - 3)/5
2. f(x) = 4/5x
- x = 4/5y ⇒ y = 5/4x
- f⁻¹(x) = 5/4x
3. f(x) = (2x + 7)/4
- x = (2y + 7)/4 ⇒ 2y + 7 = 4x ⇒ 2y = 4x - 7 ⇒ y = 2x - 3.5
- f⁻¹(x) = 2x - 3.5
4. f(x) = (2x + 7) /(x + 3) = 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. f(x) = [tex]\sqrt{x - 4}[/tex]
- x = [tex]\sqrt{y - 4}[/tex] ⇒ x² = y - 4 ⇒ y = x² + 4
- f⁻¹(x) = x² + 4
