Questions: Given that f(x)=5x+4 and g(x)=1-x^2, calculate (a) (f o g)(3)= (b) (g o f)(3)= (c) (f o f)(3)= (d) (g o g)(3)=

Transcript text: Given that $f(x)=5 x+4$ and $g(x)=1-x^{2}$, calculate (a) $(f \circ g)(3)=$ $\square$ (b) $(g \circ f)(3)=$ $\square$ (c) $(f \circ f)(3)=$ $\square$ (d) $(g \circ g)(3)=$ $\square$

Solution

Solution Steps

Step 1: Finding the composition $(f \circ g)(x)$

First, evaluate $g(3) = -8$. Then, substitute this into $f(x)$ to get $f(g(3)) = -36$. After simplification, $(f \circ g)(3) = -36$.

Step 2: Finding the composition $(g \circ f)(x)$

First, evaluate $f(3) = 19$. Then, substitute this into $g(x)$ to get $g(f(3)) = -360$. After simplification, $(g \circ f)(3) = -360$.

Final Answer:

The composition $(f \circ g)(3)$ is approximately -36 when rounded to 2 decimal places. The composition $(g \circ f)(3)$ is approximately -360 when rounded to 2 decimal places.

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