Question

Please help me Which of the following is the inverse of the function given below?

Answer 1

Answer:

Option A.

Step-by-step explanation:

The given function is

$f(x)=\dfrac{x+2}{7}$

Step 1: Substitute f(x)=y.

$y=\dfrac{x+2}{7}$

Step 2: Interchange x and y.

$x=\dfrac{y+2}{7}$

Step 3: Isolate y.

$7x=y+2$

$7x-2=y$

Step 4: Substitute $y=f^{-1}(x)$

$7x-2=f^{-1}(x)$

$f^{-1}(x)=7x-2$

The inverse of the given function is $p=7x-2$.

Therefore, the correct option is A.

Answer 2

The function is described by the rule $f(x)= \frac{x+2}{7}$.

The inverse function $f^{-1}$ is such that $f(f^{-1}(x))=x$.

Thus, since $f(x)= \frac{x+2}{7}$, we have $f(f^{-1}(x))=\frac{f^{-1}(x)+2}{7}$.

Equating the two ways we expressed $f(f^{-1}(x))$, we have:

$\displaystyle{ \frac{f^{-1}(x)+2}{7}=x$.

Rearranging, we have: 

                                       
 $\displaystyle{ f^{-1}(x)= 7x-2$.



Answer: first choice: p(x)=7x-2