Answer :
To solve this problem, we need to evaluate the given function based on the two parts of the question:
(i) Find [tex]f\left(\frac{1}{7}\right)[/tex]:
Given the function [tex]f(x) = 7x - 6[/tex], we can find [tex]f\left(\frac{1}{7}\right)[/tex] by substituting [tex]x = \frac{1}{7}[/tex] into the function.
[tex]f\left(\frac{1}{7}\right) = 7 \times \frac{1}{7} - 6[/tex]
Simplifying inside the function:
[tex]f\left(\frac{1}{7}\right) = 1 - 6[/tex]
Therefore:
[tex]f\left(\frac{1}{7}\right) = -5[/tex]
(ii) Find the value of [tex]x[/tex] for which [tex]f(x) = 71[/tex]:
We need to solve for [tex]x[/tex] in the equation [tex]f(x) = 71[/tex].
Starting with the function definition:
[tex]7x - 6 = 71[/tex]
First, add 6 to both sides to isolate the term with [tex]x[/tex]:
[tex]7x = 71 + 6[/tex]
[tex]7x = 77[/tex]
Now, divide both sides by 7 to solve for [tex]x[/tex]:
[tex]x = \frac{77}{7}[/tex]
[tex]x = 11[/tex]
Therefore, the value of [tex]x[/tex] for which [tex]f(x) = 71[/tex] is [tex]x = 11[/tex].
