QuestionFor $f(x)=7 x-6$ and $g(x)=\frac{1}{7}(x+6)$, find $(f \circ g)(x)$ and $(g \circ f)(x)$. Then determine whether $(f \circ g)(x)=(g \circ f)(x)$.
What is $(f \circ g)(x)$ ? $$(f \circ g)(x)=$$

Studdy Solution
Simplify the expression:
$$7\left(\frac{1}{7}(x + 6)\right) = x + 6$$
Thus:
$$f\left(\frac{1}{7}(x + 6)\right) = x + 6 - 6$$ $$f\left(\frac{1}{7}(x + 6)\right) = x$$
So, $(f \circ g)(x) = x$.
The value of $(f \circ g)(x)$ is:
$$(f \circ g)(x) = x$$