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Find the inverse of each function:
g(x)=[tex]\frac{-5x+5}{2}[/tex]
A. g^{-1}[/tex](x)=[tex]\frac{5-2x}{5}[/tex]
B. g^{-1}[/tex](x)=[tex]4+\frac{4}{3}x[/tex]
C. g^{-1}[/tex](x)=[tex]\frac{10-x}{2}[/tex]
D. g^{-1}[/tex](x)=[tex]-4+\frac{1}{3}x[/tex]

Respuesta :

GeorgePP

Answer:

Step-by-step explanation:

Replace g(x) with y, then switch the x and y variables:

[tex]x=\frac{-5y+5}{2}[/tex]

Solve for the new y value, multiply by 2:

[tex]2x=-5y+5[/tex]

Subtract 5 on both sides:

[tex]2x-5=-5y[/tex]

Divide by -5 on both sides:

[tex]-\frac{2x-5}{5} =y[/tex]

Distribute the negative sign and rearrange:

[tex]\frac{-2x+5}{5} =\frac{5-2x}{5} =g^-^1(x)[/tex]

mhanifa

Answer:

  • A. g⁻¹(x) = (5 - 2x)/5

Step-by-step explanation:

Given function

  • g(x) = (-5x + 5)/2

Find

  • the inverse of g(x)

Solution

Substitute x with y and g(x) with x and  then solve for y:

  • x = (-5y + 5) /2
  • 2x = -5y + 5
  • 5y = -2x + 5
  • y = (-2x + 5)/5
  • y = (5 - 2x)/5

Replace y with g⁻¹(x)

  • g⁻¹(x) = (5 - 2x)/5

Correct choice is A