Question

For a given input value a, the function h outputs a value b to satisfy the following equation3a - 5 = -4b + 1Write a formula for h(a) in terms of a.

Answer 1

We know that function h outputs the value of b when we input a value of a, that means:

`b=h(a)`

To find the expression for h we just need to solve the equation given for b, let's do that:

`\begin{gathered} 3a-5=-4b+1 \\ -4b=3a-5-1 \\ -4b=3a-6 \\ b=(3a-6)/(-4) \\ b=-(3)/(4)a+(6)/(4) \\ b=-(3)/(4)a+(3)/(2) \end{gathered}`

Therefore, we have that:

`h(a)=-(3)/(4)a+(3)/(2)`