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:

$\begin{gathered} 3a-5=-4b+1 \\ -4b=3a-5-1 \\ -4b=3a-6 \\ b=\frac{3a-6}{-4} \\ b=-\frac{3}{4}a+\frac{6}{4} \\ b=-\frac{3}{4}a+\frac{3}{2} \end{gathered}$

Therefore, we have that:

$h(a)=-\frac{3}{4}a+\frac{3}{2}$