Question

Find the inverse of each function:

Answer 1

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

Answer 2

Answer:

Step-by-step explanation:

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

$x=\frac{-5y+5}{2}$

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:

$-\frac{2x-5}{5} =y$

Distribute the negative sign and rearrange:

$\frac{-2x+5}{5} =\frac{5-2x}{5} =g^-^1(x)$