Questions: Find f ∘ g, g ∘ f, and g ∘ g. f(x) = 3x, g(x) = x^4 (a) f ∘ g (b) g ∘ f (c) g ∘ g

Transcript text: Find $f \circ g, g \circ f$, and $g \circ g$. \[ f(x)=3 x, \quad g(x)=x^{4} \] (a) $f \circ g$ $\square$ (b) $g \circ f$ $\square$ (c) $g \circ g$ $\square$

Solution

Solution Steps

Step 1: Find $f \circ g$

To find $f \circ g$, we substitute $g(x) = x^4$ into $f(x) = 3_x$, obtaining $f(g(x)) = 3_x^4$.

Step 2: Find $g \circ f$

To find $g \circ f$, we substitute $f(x) = 3_x$ into $g(x) = x^4$, obtaining $g(f(x)) = 81_x^4$.

Step 3: Find $g \circ g$

To find $g \circ g$, we substitute $g(x)$ into itself, obtaining $g(g(x)) = x^16$.

Final Answer:

The compositions are $f \circ g = 3_x^4$, $g \circ f = 81_x^4$, and $g \circ g = x^16$.

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