Set, Relations and FunctionsMTP May 19 Series IIQuestion 1986 of 217
All Questions

Find the f∘g\displaystyle f \circ g for the functions f(x)=x2\displaystyle f(x) = x^2, g(x)=x+1\displaystyle g(x) = x+1.

Options

Ax2(x+1)\displaystyle x^2(x+1)
B(x+1)2\displaystyle (x+1)^2
Cx2+1\displaystyle x^2+1
D(x+1)2\displaystyle (x+1)^2
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Correct Answer

✅ Option d — (x+1)2\displaystyle (x+1)^2

All Options:

  • Ax2(x+1)\displaystyle x^2(x+1)
  • B(x+1)2\displaystyle (x+1)^2
  • Cx2+1\displaystyle x^2+1
  • D(x+1)2\displaystyle (x+1)^2

Detailed Solution & Explanation

To find the composite function (f∘g)(x)=f(g(x))\displaystyle (f \circ g)(x) = f(g(x)), we substitute g(x)\displaystyle g(x) into f(x)\displaystyle f(x):
Given:
f(x)=x2f(x) = x^2
g(x)=x+1g(x) = x + 1

Substitute g(x)\displaystyle g(x) in place of x\displaystyle x in the function f(x)\displaystyle f(x):
f(g(x))=(g(x))2f(g(x)) = (g(x))^2
Substitute g(x)=x+1\displaystyle g(x) = x + 1:
f(g(x))=(x+1)2f(g(x)) = (x + 1)^2

Both **Option B** and **Option D** are listed identically as (x+1)2\displaystyle (x + 1)^2. The designated correct option in the answer key is **Option D**.

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

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