Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Functions

NDA 2015 · Mathematics · Functions

If f: R arrow R, g: R arrow R be two functions given by f(x)=2 x-3...

If f:R→R,g:R→Rf: R \rightarrow R, g: R \rightarrow R be two functions given by f(x)=2x−3f(x)=2 x-3 and g(x)=x3+5g(x)=x^3+5, then (f∘g)−1(x)(f {}^{\circ} g)^{-1}(x) is equal to

Options

  1. A(x+72)13\left(\frac{x+7}{2}\right)^{\frac{1}{3}}
  2. B(x−72)13\left(\frac{x-7}{2}\right)^{\frac{1}{3}}
  3. C(x−72)13\left(x-\frac{7}{2}\right)^{\frac{1}{3}}
  4. D(x+72)13\left(x+\frac{7}{2}\right)^{\frac{1}{3}}

Correct answer

B. (x−72)13\left(\frac{x-7}{2}\right)^{\frac{1}{3}}

Step-by-step solution

f(x)=2x−3g(x)=x3+5fog⁡(x)=f[g(x)]=f(x3+5)=2(x3+5)−3fog⁡(x)=2x3+7=y( say )\begin{aligned} & f(x)=2 x-3 \\ & g(x)=x^3+5 \\ & \operatorname{fog}(x)=f[g(x)]=f\left(x^3+5\right) \\ & =2\left(x^3+5\right)-3 \\ & \operatorname{fog}(x)=2 x^3+7=y(\text{ say })\end{aligned}⇒2x3=y−7⇒x=[y−72]13⇒fog⁡−1(y)=[y−72]13⇒fog⁡−1(x)=[x−72]13\begin{aligned} & \Rightarrow 2 x^3=y-7 \\ & \Rightarrow \quad x=\left[\frac{y-7}{2}\right]^{\frac{1}{3}} \\ & \Rightarrow \quad \operatorname{fog}^{-1}(y)=\left[\frac{y-7}{2}\right]^{\frac{1}{3}} \\ & \Rightarrow \quad \operatorname{fog}^{-1}(x)=\left[\frac{x-7}{2}\right]^{\frac{1}{3}}\end{aligned}$
Practice Functions on Quantrex Academy →

More from Functions

Consider the following statements in respect of the function f(x)=x in the interval… NDA 2026Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the number of points of… NDA 2026If 2f(x)+f(1-x)=x , then what is f(x) equal to ? NDA 2026For the following two (02) items: Consider the function f(x) = 1 - [3] (x-1)^2 . What is… NDA 2025Consider the following for the two (02) items that follow: Let the function y = (1 - x)^… NDA 2025For the following two (02) items: Consider the function f(x) = 10^x - 10^ -x 10^x + 10^… NDA 2025Consider the following for the two (02) items that follow: Let the curve f(x) = |x - 3| .… NDA 2025Consider the following for the two (02) items that follow: Let f = \ (1,1), (2,4), (3,7)… NDA 2025For the following two (02) items: Consider the function f(x) = (x)/(1 - x) (x > 0 , x ≠ 1… NDA 2025Consider the following for the two (02) items that follow: The function f(x) satisfies… NDA 2025Consider the following for the two (02) items that follow: The function f(x) satisfies… NDA 2025Consider the following for the two (02) items that follow: A function f is such that… NDA 2025For the following two (02) items: Consider the function f(x) = (x)/(1 - x) (x > 0 , x ≠ 1… NDA 2025For the following two (02) items: Consider the function f(x) = 10^x - 10^ -x 10^x + 10^… NDA 2025Consider the following for the two (02) items that follow: Let f = \ (1,1), (2,4), (3,7)… NDA 2025Consider the following for the two (02) items that follow: A function f is such that… NDA 2025 Full Functions list Functions JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs