A) \[3+{{(1-x)}^{7/4}}\]
B) \[3+{{(1-{{x}^{4}})}^{7}}\]
C) \[3+{{(1-{{x}^{7}})}^{1/4}}\]
D) \[3-{{(1-{{x}^{4}})}^{1/7}}\]
Correct Answer: C
Solution :
Let\[y=f(x)={{[1-{{(x-3)}^{4}}]}^{1/7}}\] \[\Rightarrow \] \[{{y}^{7}}=1-{{(x-3)}^{4}}\] \[\Rightarrow \] \[{{(x-3)}^{4}}=1-{{y}^{7}}\] \[\Rightarrow \] \[x=3+{{(1-{{y}^{7}})}^{1/4}}\] \[\Rightarrow \] \[{{f}^{-1}}(y)=3+{{(1-{{y}^{7}})}^{1/4}}\] \[\Rightarrow \] \[{{f}^{-1}}(x)=3+{{(1-{{x}^{7}})}^{1/4}}\]
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