Question

If $f(x)={[1-{(x-3)}^4]}^{1/7}$ , find $f^{-1}(x)$ .

• A. $3+{(1-x)}^{7/4}$
• B. $3+{(1-x^4)}^7$
• C. $3+{(1-x^7)}^{1/4}$
• D. $3-{(1-x^4)}^{1/7}$

Answer 1

Answer: (C)

Let $y=f(x)={[1-{(x-3)}^4]}^{1/7}$
$\Rightarrow$ $y^7=1-{(x-3)}^4$
$\Rightarrow$ ${(x-3)}^4=1-y^7$
$\Rightarrow$ $x=3+{(1-y^7)}^{1/4}$
$\Rightarrow$ $f^{-1}(y)=3+{(1-y^7)}^{1/4}$
$\Rightarrow$ $f^{-1}(x)=3+{(1-x^7)}^{1/4}$