# If f(x) = (√x)/3 , then f ^-1 (x) =Please help me im stuck and have no idea how to solve it. Thanks.

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f(x) = (√x)/3 , then f ^-1 (x) =

We have the function f(x) = sqrtx/ 3

We need to find the inverse f^-1 (x)

==>let y = sqrtx / 3

Let us multiply by 3:

==> 3y = sqrtx

Now we will square both sides:

==> (3y)^2 = x

==> x= 9y^2

Now we will rewrite x and y and y as x:

==> y = 9x^2

Then, the inverse of the function f(x) is:

**f^-1 (x) = 9x^2 **

We have the function f(x) = ( sqrt x)/3.

Now we need to find the iverse of teh function f(x) = (sqrt x)/3.

Let f(x) = (sqrt x)/3 = y

square both the sides

=> x / 9 = y^2

=> x = 9y^2

Replace x with y and vice versa.

**We get the inverse function of f(x) = ( sqrt x)/3 as f(x) = 9x^2.**

f(x) =( sqrtx)/3.

To find the f^-1(x).

Solution:

Let f^-1 (x) = be y.

Then by defintion. x = f(y).

Therefore by definition if f unction f(x) = (sqrtx)/3,

f(y) = (sqrty)/3.

x = (sqrty)/3

Now we solve for y by squaring both sides:

x^2 = y/ 9

Therefore y = x^2/9 .

Therefore the inverse of f(x) = (sqrtx)/3 is y = x^2/9.

Each time when we want to determine the inverse function, we'l have to writ x with respect to y.

We'll note f(x) = y and we'll re-write:

y = (√x)/3

We'll multiply both sides by 3:

3y = (√x)

We'll raise to square both sides, to get rid off the square root:

(3y)^2 = x

We'll use the symmetric property:

x = 9y^2

**So, f^-1(x) = 9x^2**