Set, Relations and FunctionsMTP Sep 24 Series I/ RTP Sep 24Question 2006 of 217
All Questions

If f(x)=x+2,g(x)=7x\displaystyle f(x)=x+2, g(x)=7^x, then g∘f(x)=\displaystyle g \circ f(x)=

Options

A7x.x+2.7x\displaystyle 7x.x+2.7x
B7x+2\displaystyle 7x+2
C49(7x)\displaystyle 49(7x)
DNone of these
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Correct Answer

✅ Option c — 49(7x)\displaystyle 49(7x)

All Options:

  • A7x.x+2.7x\displaystyle 7x.x+2.7x
  • B7x+2\displaystyle 7x+2
  • C49(7x)\displaystyle 49(7x)
  • 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 exponent laws:
7x+2=7x⋅72=49(7x)7^{x+2} = 7^x \cdot 7^2 = 49(7^x)

**Discrepancy & Printing Error:**
The mathematical value of the composition is 49(7x)\displaystyle 49(7^x). However, the exam options contain a typographical error where the exam printed multiplication instead of exponents (e.g., 7x\displaystyle 7x instead of 7x\displaystyle 7^x, leading to Option C being printed as 49(7x)\displaystyle 49(7x) instead of 49(7x)\displaystyle 49(7^x)). Under this typographic corruption, **Option C** remains the designated correct option.

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

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