Use composition to verify whether or not the inverse is correct.
-$$f ( x ) = - \frac { 1 } { 8 } x , f ^ { - 1 } ( x ) = - 8 x$$

Question

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To verify if $f^{-1}(x) = -8x$ is the correct inverse of $f(x) = -\frac{1}{8}x$, we can use composition: $f(f^{-1}(x))$ and $f^{-1}(f(x))$ should both equal $x$. For $f(f^{-1}(x))$, we substitute $f^{-1}(x) = -8x$ into $f(x)$, getting $f(-8x) = -\frac{1}{8}(-8x) = x$. Similarly, for $f^{-1}(f(x))$, substituting $f(x) = -\frac{1}{8}x$ into $f^{-1}(x)$, we get $f^{-1}(-\frac{1}{8}x) = -8(-\frac{1}{8}x) = x$. Since both compositions return $x$, $f^{-1}(x) = -8x$ is indeed the correct inverse of $f(x) = -\frac{1}{8}x$.

Use Composition to Verify Whether or Not the Inverse Is f(x)=−18x,f−1(x)=−8xf ( x ) = - \frac { 1 } { 8 } x , f ^ { - 1 } ( x ) = - 8 xf(x)=−81​x,f−1(x)=−8x

Use Composition to Verify Whether or Not the Inverse Is $f ( x ) = - \frac { 1 } { 8 } x , f ^ { - 1 } ( x ) = - 8 x$