Relations and Functions — Class 12 Maths Solution

exemplar objective MCQ NCERT Exemp.Q.40,Page 15
Question

If $f:R \to R$ be the functions defined by $f(x) = {x^3} + 5$, then ${f^{ - 1}}(x)$ is

  • (a) ${(x + 5)^{\frac{1}{3}}}$
  • (b) ${(x - 5)^{\frac{1}{3}}}$ ✓ Correct
  • (c) ${(5 - x)^{\frac{1}{3}}}$
  • (d) $5 - x$
Step-by-step Solution
Correct answer: option (b)

It is given that,, $f(x) = {x^3} + 5$

Let $y = {x^3} + 5 \Rightarrow {x^3} = y - 5$

$x = {(y - 5)^{\frac{1}{3}}} \Rightarrow f{(x)^{ - 1}} = {(x - 5)^{\frac{1}{3}}}$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Relations and Functions. Curated by Sachin Sharma. Free for all students.