Find the inverse of the given function and express it in the form $y = f ^ { - 1 } ( x )$ . Verify the result by showing that $\left( f \circ f ^ { - 1 } \right) ( x ) = \left( f ^ { - 1 } \circ f \right) ( x ) = I ( x )$ . $f ( x ) = \frac { 2 x + 10 } { 5 }$
A) $f ^ { - 1 } ( x ) = 5 x - 2$
B) $f ^ { - 1 } ( x ) = \frac { 5 } { 2 } x - 5$
C) $f ^ { - 1 } ( x ) = \frac { 2 } { 5 } x + 2$
D) $f ^ { - 1 } ( x ) = \frac { 5 } { 2 } x + 5$
E) $f ^ { - 1 } ( x ) = 2 x + 5$

Question

Quizplus · Accepted Answer

To find the inverse of $f(x) = \frac{2x + 10}{5}$, we swap $x$ and $y$ and solve for $y$. So, we start with $x = \frac{2y + 10}{5}$, multiply both sides by 5 to get $5x = 2y + 10$, and then solve for $y$ to get $y = \frac{5}{2}x - 5$, which matches choice B. Verification involves composing $f$ and $f^{-1}$ in both orders and showing the result is the identity function $I(x) = x$.

Find the Inverse of the Given Function and Express It y=f−1(x)y = f ^ { - 1 } ( x )y=f−1(x)

Find the Inverse of the Given Function and Express It $y = f ^ { - 1 } ( x )$