For the given function f(x), find f-1(x).
-$$f ( x ) = \frac { 1 } { 3 } x + 7$$
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 3 \mathrm { x } - 21$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 7 } \mathrm { x } + 3$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 3 \mathrm { x } + 21$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 3 } x - 7$

Question

Quizplus · Accepted Answer

To find the inverse function $f^{-1}(x)$, swap $x$ and $y$ in the original function and solve for $y$. Starting with $y = \frac{1}{3}x + 7$, swapping gives $x = \frac{1}{3}y + 7$. Solving for $y$ gives $y = 3x - 21$, which matches choice A.

For the Given Function F(x), Find F-1(x) f(x)=13x+7f ( x ) = \frac { 1 } { 3 } x + 7f(x)=31​x+7

For the Given Function F(x), Find F-1(x) $f ( x ) = \frac { 1 } { 3 } x + 7$