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

• A. 16
• B. 18
• C. 36
• D. 40

Answer 1

The Correct Option is C

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.