Question

given the one - to - one function ( f(x)=x^{3}+9 ) find the following hint you do not need to find the equation for ( f^{-1}(x) ).
a. ( f(-1) )
b. ( f^{-1}(8) )
a. find the following value.
( f(-1)=square )
b. find the following value
( f^{-1}(8)=square )

Explanation:

Step1: Calculate \( f(-1) \)

Substitute \( x = -1 \) into \( f(x) = x^3 + 9 \).
\( f(-1) = (-1)^3 + 9 = -1 + 9 = 8 \)

Step2: Calculate \( f^{-1}(8) \)

Since \( f \) is one - to - one, if \( f(a)=b \), then \( f^{-1}(b)=a \). We found that \( f(-1) = 8 \), so \( f^{-1}(8)=-1 \)

Answer:

a. \( 8 \)
b. \( -1 \)