a) The output is 45
b) The input was -4
Here, we want to use the relationship between the input and the output to answer the questions
While x is our input, f(x) is given as our output
The relationship between the two is given as;
[tex]f(x)\text{ = -6x-3}[/tex]
a) Here, we have an input, and we want to get the output
To solve this, we just need to substitute the value of -8 for x in the relation
We have this as follows;
[tex]\begin{gathered} f(-8)\text{ = -6(-8)-3} \\ f(-8)\text{ = 48-3 = 45} \end{gathered}[/tex]
b) Here, we have the output, but we want to get the input
What this simply mean is that we are to find the value of x
We simply substitute 21 for f(x)
Thus, we have;
[tex]\begin{gathered} 21\text{ = -6x-3} \\ 21\text{ + 3 = -6x} \\ \\ -6x\text{ = 24} \\ \\ x\text{ = }\frac{24}{-6} \\ \\ x\text{ = -4} \end{gathered}[/tex]
