Use composition to verify whether or not the inverse is correct.
-$$f ( x ) = 3 x + 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3$$

Question

Quizplus · Accepted Answer

To verify if $f^{-1}(x) = \frac{1}{3}x - 3$ is the correct inverse of $f(x) = 3x + 9$, we can use composition in both orders: $f(f^{-1}(x))$ and $f^{-1}(f(x))$. For $f(f^{-1}(x))$, substituting $f^{-1}(x)$ into $f(x)$ gives $f\left(\frac{1}{3}x - 3\right) = 3\left(\frac{1}{3}x - 3\right) + 9 = x$. For $f^{-1}(f(x))$, substituting $f(x)$ into $f^{-1}(x)$ gives $f^{-1}(3x + 9) = \frac{1}{3}(3x + 9) - 3 = x$. Since both compositions result in $x$, $f^{-1}(x) = \frac{1}{3}x - 3$ is indeed the correct inverse of $f(x) = 3x + 9$.

Use Composition to Verify Whether or Not the Inverse Is f(x)=3x+9,f−1(x)=13x−3f ( x ) = 3 x + 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3f(x)=3x+9,f−1(x)=31​x−3

Use Composition to Verify Whether or Not the Inverse Is $f ( x ) = 3 x + 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3$