Question

If \( \varphi(x) = x^2 \) and \( \psi(x) = 2^x \), then \( \psi(\varphi(x)) \) is

• A. \( 2^{x^2}\)
• B. \( x^2 \)
• C. \( 2^{2x} \)
• D. \( x^{2x} \)

Hint:

When composing functions, substitute one function into another and simplify the result.

Answer 1

The Correct Option is A

Step 1: Understanding the composition of functions. 
We are asked to find \( \psi(\varphi(x)) \), which means we need to substitute \( \varphi(x) = x^2 \) into \( \psi(x) = 2^x \). This gives us: \[ \psi(\varphi(x)) = 2^{\varphi(x)} = 2^{x^2} \]

Step 2: Conclusion. 
The correct answer is (A) \( 2^{x^2}\) , as this is the result of the composition of \( \psi(x) \) and \( \varphi(x) \).