Question:
Let f(x) = x2 and g(x) = 2X , for all real x. Then the value of f( f(g(x)) + g(f(x)) ) at x = 1 is
Let f(x) = x2 and g(x) = 2X , for all real x. Then the value of f( f(g(x)) + g(f(x)) ) at x = 1 is
Updated On: Jul 29, 2025
- 16
- 18
- 36
- 40
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The Correct Option is C
Solution and Explanation
To solve the problem, we need to evaluate the expression \( f( f(g(x)) + g(f(x)) ) \) at \( x = 1 \). Here are the steps:
- First, define the functions \( f(x) = x^2 \) and \( g(x) = 2x \).
- Calculate \( g(x) \) at \( x = 1 \):
\( g(x) = 2x \rightarrow g(1) = 2 \times 1 = 2 \)
- Calculate \( f(x) \) at \( x = 1 \):
\( f(x) = x^2 \rightarrow f(1) = 1^2 = 1 \)
- Now, calculate \( f(g(x)) \):
\( f(g(x)) = f(2) = 2^2 = 4 \)
- Calculate \( g(f(x)) \):
\( g(f(x)) = g(1) = 2 \times 1 = 2 \)
- Add the results of step 3 and step 4:
\( f(g(x)) + g(f(x)) = 4 + 2 = 6 \)
- Finally, evaluate \( f(6) \):
\( f(6) = 6^2 = 36 \)
Thus, the value of \( f( f(g(x)) + g(f(x)) ) \) at \( x = 1 \) is 36.
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