Use $f (x) = 5 x - 3$ and $g (x) = 2 - x^{2}$ to evaluate the expression.
(a) $(f \circ f) (x)$
(b) $(g \circ g) (x)$

Answer

Expert–verified

Hide Steps

Answer

Final Answer: (a) $(f \circ f) (x) = 25 x - 18$ , (b) $(g \circ g) (x) = 2 - (2 - x^{2})^{2}$

Steps

Step 1 ：Given the functions $f (x) = 5 x - 3$ and $g (x) = 2 - x^{2}$ , we are asked to evaluate the expressions $(f \circ f) (x)$ and $(g \circ g) (x)$ .

Step 2 ：The composition of two functions, $f$ and $g$ , denoted as $(f \circ g) (x)$ , is defined as $f (g (x))$ .

Step 3 ：For part (a), we need to find $(f \circ f) (x)$ , which means we need to substitute $f (x)$ into itself. So, $(f \circ f) (x) = f (f (x)) = f (5 x - 3) = 5 (5 x - 3) - 3 = 25 x - 15 - 3 = 25 x - 18$ .

Step 4 ：For part (b), we need to find $(g \circ g) (x)$ , which means we need to substitute $g (x)$ into itself. So, $(g \circ g) (x) = g (g (x)) = g (2 - x^{2}) = 2 - (2 - x^{2})^{2}$ .

Step 5 ：Final Answer: (a) $(f \circ f) (x) = 25 x - 18$ , (b) $(g \circ g) (x) = 2 - (2 - x^{2})^{2}$

Use f(x)=5x−3 and g(x)=2−x2 to evaluate the expression.(a) (f∘f)(x)(b) (g∘g)(x)

Answer

Popular Problems

Use $f (x) = 5 x - 3$ and $g (x) = 2 - x^{2}$ to evaluate the expression.
(a) $(f \circ f) (x)$
(b) $(g \circ g) (x)$