Question

Question 8 of 25 Which pair of functions are inverses of each other? O A. Rx) = 7x - 2 and g(x) = =+2 B. f(2) and g(x) = 6x3 15 O c. f(x) = - 2 and g(x) 2 – = O D. f(x) = 1 + 6 and g(x) = 5x - 6

Answer 1

To chech if 2 functions are inverses of each other we must invert the variables like this

$\frac{x}{2}=y\rightarrow\frac{y}{2}=x$

after inverting the variables we clear the new function for y and that will be the inverse

$\begin{gathered} \frac{y}{2}=x \\ y=2x \end{gathered}$

after this we can conclude that

$\begin{gathered} f(x)=\frac{x}{2} \\ f^{-1}(x)=2x \end{gathered}$

After this we can say that in function A this is been fulfilled

$\begin{gathered} y=7x-2\rightarrow x=7y-2 \\ \text{clear for y} \\ x+2=7y \\ y=\frac{x+2}{7} \end{gathered}$