Question

Consider function f.

f(1) = 170 – 21
Place the steps for finding /-(s) in the correct order.
y = 171 – 21
I = V7y - 21
1
432 + 3 = 1-1(), where I > 0
1
(1 +21)2 = 77
$(72 – 21) = |-|(s), where a > 0
1
12 + 21 = 7y
12 = 7y - 21
1
42 +3 = 4
1

Answer 1

Given:

The function is:

`f(x)=√(7x-21)`

To find:

The steps of finding the inverse function
`f^(-1)(x)`.

Solution:

We have,

`f(x)=√(7x-21)`

The steps of finding the inverse function are:

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

`y=√(7x-21)`

Step 2: Interchange x and y.

`x=√(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.

`(1)/(7)x^2+3=y`

Step 6: Substitute
`y=f^(-1)(x)`.

`(1)/(7)x^2+3=f^(-1)(x)`, where
`x\geq 0`.

Therefore, the inverse of the given function is
`f^(-1)(x)=(1)/(7)x^2+3` and the arrangement of steps is shown above.