Question

For a given input value a, the function f outputs a value b to satisfy the following equation: −3a+6b=a+4b. Write a formula for f(a) in terms of a.

A) f(a)=−3a
B) f(a)=9a
C) f(a)=6a
D) f(a)=−6a

Answer 1

The formula for the function f(a) in terms of a is f(a) = 2a.

Step-by-step explanation:

Given the equation −3a+6b=a+4b, we can solve for b in terms of a.

Start by combining like terms:

-3a + 6b = a + 4b

Subtract 4b from both sides:

-3a + 6b - 4b = a

Combine like terms again:

-3a + 2b = a

Now, isolate b by subtracting a from both sides:

2b = a + 3a

Combine like terms:

2b = 4a

Finally, solve for b by dividing both sides by 2:

b = 2a

Therefore, the function f(a) in terms of a is f(a) = 2a.