Question

For a given input value b, the function f outputs a value a to satisfy the following equation. 4a+7b=−52 Write a formula for ) f(b) in terms of b.

Answer 1

`f(b)=(-52-7b)/(4)`

Explanation:

The given equation is

`4a+7b=-52`

where, b is the input value and a is the output value of function f.

We need to find the formula for f(b) in terms of b.

It means we have to separate
`a` on one side because
`a=f(b)`.

Consider the given equation.

`4a+7b=-52`

Subtract 7b from both sides.

`4a+7b-7b=-52-7b`

`4a=-52-7b`

Divide both sides by 4.

`a=(-52-7b)/(4)`

Substitute a=f(b).

`f(b)=(-52-7b)/(4)`

Therefore, the required formula is
`f(b)=(-52-7b)/(4)`.

Answer 2

Answer: Our required formula becomes :

`a=f(b)=-13-(7)/(4)b`

Explanation:

Since we have given that

`4a+7b=-52\\`

We need to write a formula for f(b) in terms of b So, it becomes

`4a=-52-7b\\\\a=(-52-7b)/(4)\\\\a=(-52)/(4)-(7b)/(4)\\\\a=-13-(7b)/(4)`

Hence, our required formula becomes :

`a=f(b)=-13-(7)/(4)b`