Question

Which function below is the inverse of f(x) = X2 - 25?

Answer 1

Answer: $f^{-1}(x)= \sqrt{x+25}$ and $f^{-1}(x)= - \sqrt{x+25}$

Step-by-step explanation:

   To find the inverse, we will set f(x) equal to y, swap the x and y values, and then solve for y.

   Given:

f(x) = x² - 25

   Equal to y:

y = x² - 25

   Swamp x and y values:

x = y² - 25

   Add 25 to both sides of the equation:

y² = x + 25

   Square root both sides of the equation:

$y= \sqrt{x+25}$ and $y= -\sqrt{x+25}$

   Interval notation:

$f^{-1}(x)= \sqrt{x+25},\text{and}\;f^{-1}(x)= -\sqrt{x+25}$

Answer 2

⇒Note for inverses we swap the positions between x and y.

⇒$x=y^{2} -25$

But in this case we know that we write the equation such that the variable for the input is the subject of the equation

$y^{2}= x+25\\y=\sqrt{x+25}$

Note y in this case was representing f(x)

⇒therefore our final equation now is

$f(x)=\sqrt{x+25}$

GOODLUCK!!!