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

Answer:

$f(b)=\dfrac{-52-7b}{4}$

Step-by-step 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.

$a=\dfrac{-52-7b}{4}$

Substitute a=f(b).

$f(b)=\dfrac{-52-7b}{4}$

Therefore, the required formula is $f(b)=\dfrac{-52-7b}{4}$.

Answer 2

Answer: Our required formula becomes :

$a=f(b)=-13-\frac{7}{4}b$

Step-by-step 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

$4a=-52-7b\\\\a=\frac{-52-7b}{4}\\\\a=\frac{-52}{4}-\frac{7b}{4}\\\\a=-13-\frac{7b}{4}$

Hence, our required formula becomes :

$a=f(b)=-13-\frac{7}{4}b$