Question

Iff(x) = (x - 3)2

for x = 3, then f-1(x) = ?
A
VX-3
B.
√x+3
O
a VX-3
IN x + 3

Answer 1

Option B. √x + 3

Explanation:

f(x) = (x - 3)²

We can obtain the inverse f¯¹(x) of the above expression as follow:

f(x) = (x - 3)²

Replace f(x) with

f(x) = (x - 3)²

y = (x - 3)²

Next, interchange x and y

y = (x - 3)²

x = (y - 3)²

Make y the subject

x = (y - 3)²

Take the square root of both side

√x = y - 3

Add 3 to both side

√x + 3 = y - 3 +3

√x + 3 = y

y = √x + 3

Finally, replace y with f¯¹(x)

y = √x + 3

f¯¹(x) = √x + 3