Final answer:
To find the inverse of h(x) = 7x - 16/9, swap the roles of x and y and solve for y using algebraic steps. The inverse function is h^-1(x) = (x + 16/9)/7.
Step-by-step explanation:
To find the inverse of a function, we need to switch the roles of x and y and solve for y. So in this case, let's start with the equation h(x) = √7x - 16/9. Step 1: Replace h(x) with y in the equation. Step 2: Swap the roles of x and y, so the equation becomes x = √7y - 16/9. Step 3: Solve for y by isolating it on one side of the equation. Step 4: Undo the square root operation by squaring both sides. Step 5: Simplify the equation by getting rid of the square root symbol. Step 6: Solve for y by isolating it on one side of the equation.
After doing all the steps, we find that the inverse function of h(x) = 7x - 16/9 is h-1(x) = (x + 16/9)/7.