Question

Which equation is the inverse of the function+f(x) = -7x-4-3A) F'(x) = -1 -2B) '(x)=-*-4172)

Answer 1

To answer this question, the first step we need to do is solve the equation for x. Then, we have:

$y=-7x-4\Rightarrow y+4=-7x\Rightarrow x=\frac{(y+4)}{-7}\Rightarrow y=-\frac{(y+4)}{7}=\frac{-y-4}{7}$

Then, changing y by x, we finally have that the inverse function is:

$f^{-1}(x)=\frac{-x-4}{7}$

To check this result, if we have that x = 1 for the first equation, the value of y is:

$y=-7(1)-4=-7-4=-11$

If we use this result in the inverse function, then we must have y = 1 ( that is the original value). That is

$f^{-1}(-11)=\text{ }\frac{-(-11)-4}{7}=\frac{11-4}{7}=\frac{7}{7}=1$

Therefore, option 3 is the answer.

Answer 2

To answer this question, the first step we need to do is solve the equation for x. Then, we have:

$y=-7x-4\Rightarrow y+4=-7x\Rightarrow x=\frac{(y+4)}{-7}\Rightarrow y=-\frac{(y+4)}{7}=\frac{-y-4}{7}$

Then, changing y by x, we finally have that the inverse function is:

$f^{-1}(x)=\frac{-x-4}{7}$

To check this result, if we have that x = 1 for the first equation, the value of y is:

$y=-7(1)-4=-7-4=-11$

If we use this result in the inverse function, then we must have y = 1 ( that is the original value). That is

$f^{-1}(-11)=\text{ }\frac{-(-11)-4}{7}=\frac{11-4}{7}=\frac{7}{7}=1$

Therefore, option 3 is the answer.