Question

Consider the function. h(x)=-(2)/(3)x+2 What is the function h^(-1)(x)? h^(-1)(x)=-(3)/(2)x-3 h^(-1)(x)=-(3)/(2)x+3 h^(-1)(x)=-(2)/(3)x-3 h^(-1)(x)=-(2)/(3)x+3

Answer 1

The inverse function of h(x) = -2/3x+2 is h^(-1)(x) = -3/2x + 3.

Step-by-step explanation:

The function h(x) is given as h(x) = -2/3x+2. To find the inverse function, we need to swap the x and y variables in the original function and solve for y. The inverse function is represented as h^(-1)(x). Start by writing the original function as y = -2/3x+2. Swap the x and y variables to get x = -2/3y+2. Now, solve for y:

x = -2/3y+2

Subtract 2 from both sides:

x - 2 = -2/3y

Divide both sides by -2/3 (or multiply both sides by -3/2) to isolate y:

y = -3/2(x - 2)

Simplify the equation:

y = -3/2x + 3

Therefore, h^(-1)(x) = -3/2x + 3.