Set, Relations and FunctionsMTP May 19Question 1984 of 217
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If f(x)=x+3\displaystyle f(x) = x+3 and g(x)=x2\displaystyle g(x) = x^2, then fog(x)\displaystyle fog(x)

Options

A(x+3)2\displaystyle (x+3)^2
Bx2+3\displaystyle x^2+3
Cx2+3\displaystyle x^2+3
DNone of these
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Correct Answer

✅ Option c — x2+3\displaystyle x^2+3

All Options:

  • A(x+3)2\displaystyle (x+3)^2
  • Bx2+3\displaystyle x^2+3
  • Cx2+3\displaystyle x^2+3
  • DNone of these

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)=x+3f(x) = x + 3
g(x)=x2g(x) = x^2

Substitute g(x)\displaystyle g(x) in place of x\displaystyle x in the definition of f(x)\displaystyle f(x):
f(g(x))=g(x)+3f(g(x)) = g(x) + 3
Substitute g(x)=x2\displaystyle g(x) = x^2:
f(g(x))=x2+3f(g(x)) = x^2 + 3

Both **Option B** and **Option C** are listed identically as x2+3\displaystyle x^2 + 3. The designated correct option in the answer key is **Option C**.

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

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