Question

let $f(x)=7x + 1$ and $g(x)=6x$. find $f \circ g$ and $g \circ f$.
a) $(f \circ g)(x)$
$(f \circ g)(x) = $
b) $(g \circ f)(x)$

Explanation:

Step1: Define composite function

$(f \circ g)(x) = f(g(x))$

Step2: Substitute $g(x)$ into $f$

$f(6x) = 7(6x) + 1$

Step3: Simplify the expression

$7(6x) + 1 = 42x + 1$

Step4: Define composite function

$(g \circ f)(x) = g(f(x))$

Step5: Substitute $f(x)$ into $g$

$g(7x+1) = 6(7x + 1)$

Step6: Simplify the expression

$6(7x + 1) = 42x + 6$

Answer:

a) $42x + 1$
b) $42x + 6$