Question

The function f is one-to-one. Find its inverse. f(x) = 3 = x + 5 of?(x) = ? 3 5 f1(x) = 1 x3 +5 Of(x) = 3 //x + 5 o f1(x) = x-5 O None of these

Answer 1

f(x) =

Step 1: Replace f(x) with y

y =

Step 2: Swap x and y

x =

Step 3: Solve for y in terms of x

=> $y = \sqrt[3]{x - 5}$

Step 4: Replace y with $f^{-1}(x)$

$f^{-1}(x) = \sqrt[3]{x - 5}$

Therefore,

$f^{-1}(x) = \sqrt[3]{x - 5}$