Given that $f (x) = | x |$ and $g (x) = 9 x + 6$ , calculate
(a) $f \circ g (x) =$
(b) $g \circ f (x) =$
(c) $f \circ f (x) =$
(d) $g \circ g (x) =$

Answer

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Answer

So, the solutions are $f (g (x)) = | 9 x + 6 |$ , $g (f (x)) = 9 | x | + 6$ , $f (f (x)) = | x |$ , and $g (g (x)) = 81 x + 60$ .

Steps

Step 1 ：First, we calculate $f (g (x))$ which is $f (9 x + 6)$ . Since $f (x)$ is the absolute value function, we have $f (g (x)) = | 9 x + 6 |$ .

Step 2 ：Next, we calculate $g (f (x))$ which is $g (| x |)$ . Substituting $| x |$ into $g (x)$ , we get $g (f (x)) = 9 | x | + 6$ .

Step 3 ：Then, we calculate $f (f (x))$ which is $f (| x |)$ . Since $f (x)$ is the absolute value function, we have $f (f (x)) = | | x | |$ , which simplifies to $| x |$ .

Step 4 ：Finally, we calculate $g (g (x))$ which is $g (9 x + 6)$ . Substituting $9 x + 6$ into $g (x)$ , we get $g (g (x)) = 9 (9 x + 6) + 6 = 81 x + 60$ .

Step 5 ：So, the solutions are $f (g (x)) = | 9 x + 6 |$ , $g (f (x)) = 9 | x | + 6$ , $f (f (x)) = | x |$ , and $g (g (x)) = 81 x + 60$ .

Given that f(x)=|x| and g(x)=9x+6, calculate(a) f∘g(x)=(b) g∘f(x)=(c) f∘f(x)=(d) g∘g(x)=

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Given that $f (x) = | x |$ and $g (x) = 9 x + 6$ , calculate
(a) $f \circ g (x) =$
(b) $g \circ f (x) =$
(c) $f \circ f (x) =$
(d) $g \circ g (x) =$