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 the terms of x

Answer 1

Answer: h(x) = $\frac{1}{5}x$

Step-by-step explanation:

6x + y = 4x + 11y

     -y            -y  

6x       = 4x + 10y

-4x        -4x        

2x       =         10y

÷10               ÷10

$\frac{1}{5}x$    =            y

Since "y" represents h(x), then h(x) = $\frac{1}{5}x$

Answer 2

According to the input relation, we isolate y, and thus, the formula for h(x) is given by:

$h(x) = 0.2x$

The input relation is:

$6x + y = 4x + 11y$

We want h(x) in terms of x, that is, we have to write y as a function of x. Then:

$11y - y = 6x - 4x$

$10y = 2x$

$y = \frac{2x}{10}$

$y = 0.2x$

Then, the formula for h(x) is:

$h(x) = 0.2x$

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