Question

For a given input value \[x\], the function \[h\] outputs a value \[y\] to satisfy the following equation. \[6x y=4x 11y\] write a formula for \[h(x)\] in terms of \[x\].

Answer 1

The function h(x) that satisfies the equation 6xy = 4x + 11y is found by isolating y and is given by h(x) = 4x / (6x - 11).

Step-by-step explanation:

The student's question is about finding the function h(x) that satisfies the equation 6xy = 4x + 11y. To solve for y as a function of x, we need to isolate y on one side of the equation.

First, we'll get all terms involving y on one side and all the terms involving x on the other:

6xy - 11y = 4x

Next, we can factor out y on the left side:

y(6x - 11) = 4x

Now, we divide both sides of the equation by (6x - 11) to solve for y:

y = 4x / (6x - 11)

This gives us the function h(x) = 4x / (6x - 11), which expresses y in terms of x.