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14 votes
Find the inverse of each function:

g(x)=
(-5x+5)/(2)
A. g^{-1}[/tex](x)=
(5-2x)/(5)
B. g^{-1}[/tex](x)=
4+(4)/(3)x
C. g^{-1}[/tex](x)=
(10-x)/(2)
D. g^{-1}[/tex](x)=
-4+(1)/(3)x

User Atli
by
8.5k points

2 Answers

4 votes

Answer:

Explanation:

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


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

Solve for the new y value, multiply by 2:


2x=-5y+5

Subtract 5 on both sides:


2x-5=-5y

Divide by -5 on both sides:


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

Distribute the negative sign and rearrange:


(-2x+5)/(5) =(5-2x)/(5) =g^-^1(x)

User DingHao
by
8.7k points
8 votes

Answer:

  • A. g⁻¹(x) = (5 - 2x)/5

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

User Netcat
by
8.7k points

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