Sets, Relations and FunctionsMCQMTP Dec 2023 Series IQuestion 2000 of 222
All Questions

If f(x)=x+2,g(x)=7x\displaystyle f(x)=x+2, g(x)=7^x, then gof(x)=\displaystyle go f(x)=

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $49(7^x)$

All Options:

  • A7x.x+2.7x\displaystyle 7^x.x+2.7^x
  • B7x+2\displaystyle 7^x+2
  • C$49(7^x)$
  • DNone of these

Detailed Solution & Explanation

To find the composite function (g∘f)(x)=g(f(x))\displaystyle (g \circ f)(x) = g(f(x)), we substitute f(x)\displaystyle f(x) into g(x)\displaystyle g(x):
Given:
f(x)=x+2f(x) = x + 2
g(x)=7xg(x) = 7^x

Substitute f(x)\displaystyle f(x) in place of x\displaystyle x in g(x)\displaystyle g(x):
g(f(x))=7f(x)=7x+2g(f(x)) = 7^{f(x)} = 7^{x + 2}
Using the algebraic exponent rule am+n=am⋅an\displaystyle a^{m+n} = a^m ⋅\displaystyle \cdot a^n, we can rewrite this as:
7x+2=7x⋅72=7x⋅49=49(7x)7^{x + 2} = 7^x ⋅\displaystyle \cdot 7^2 = 7^x ⋅\displaystyle \cdot 49 = 49(7^x)

Hence, **Option C** is the correct answer.

About This Chapter: Sets, Relations and Functions

Paper

Paper 3: Quantitative Aptitude

Weightage

3-5 Marks

Key Topics

Sets, Relations, Functions

This chapter covers Sets, Relations, Functions and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 3-5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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