Question

Consider function f.

Answer 1

Given:

The function is:

$f(x)=\sqrt{7x-21}$

To find:

The steps of finding the inverse function $f^{-1}(x)$.

Solution:

We have,

$f(x)=\sqrt{7x-21}$

The steps of finding the inverse function are:

Step 1: Substitute $f(x)=y$.

$y=\sqrt{7x-21}$

Step 2: Interchange x and y.

$x=\sqrt{7y-21}$

Step 3: Taking square on both sides, we get

$x^2=7y-21$

Step 4: Adding 21 on both sides, we get

$x^2+21=7y$

Step 5: Divide both sides by 7.

$\dfrac{1}{7}x^2+3=y$

Step 6: Substitute $y=f^{-1}(x)$.

$\dfrac{1}{7}x^2+3=f^{-1}(x)$, where $x\geq 0$.

Therefore, the inverse of the given function is $f^{-1}(x)=\dfrac{1}{7}x^2+3$ and the arrangement of steps is shown above.