Suppose f(x) = -5x + 6 and g(x) = \sqrt{x^2 - 2x + 2}.
(f \circ g)(x) =
(f \circ g)(4) =
Answer (1)
To find ( f ∘ g ) ( 4 ) , we need to evaluate the composition of the functions f ( x ) and g ( x ) . This means we'll first find g ( 4 ) and then plug that result into f ( x ) .
Step 1: Evaluate g ( 4 ) :
Given the function g ( x ) = x 2 − 2 x + 2 , substitute x = 4 :
g ( 4 ) = 4 2 − 2 × 4 + 2 Calculate inside the square root: g ( 4 ) = 16 − 8 + 2 = 10 Thus, g ( 4 ) = 10 .
Step 2: Evaluate f ( g ( 4 )) :
Next, use the function f ( x ) = − 5 x + 6 and substitute x = 10 :
f ( 10 ) = − 5 ( 10 ) + 6 Simplify the expression: f ( 10 ) = − 5 10 + 6
Therefore, ( f ∘ g ) ( 4 ) = − 5 10 + 6.
In summary, to solve ( f ∘ g ) ( 4 ) , we first evaluated g ( 4 ) as 10 , then substituted this into f ( x ) to find the final result f ( 10 ) = − 5 10 + 6 .
