Question

nd $f^{-1}(f(19)) - 2f(f(3))$.

$x$	$f(x)$
-15	3
5	9
19	1

Explanation:

Step1: Evaluate \( f^{-1}(f(19)) \)

By the property of inverse functions, \( f^{-1}(f(x)) = x \) for all \( x \) in the domain of \( f \). So when \( x = 19 \), we have \( f^{-1}(f(19)) = 19 \).

Step2: Evaluate \( f(f(3)) \)

First, find \( f(3) \) from the table. When \( x = 3 \), \( f(3)=5 \). Then, find \( f(5) \) from the table. When \( x = 5 \), \( f(5)=9 \). So \( f(f(3)) = f(5)=9 \).

Step3: Substitute into the expression

The expression is \( f^{-1}(f(19)) - 2f(f(3)) \). Substituting the values we found: \( 19 - 2\times9 \).

Step4: Calculate the result

First, calculate \( 2\times9 = 18 \). Then, \( 19 - 18 = 1 \).

Answer:

\( 1 \)