Question

Find $\varphi \left[\Psi \left(x\right)\right]$ and $\Psi \left[\varphi \left(x\right)\right]$ if $\varphi \left(x\right)=x^2+1$ and $\Psi \left(x\right)=3^x.$

• A. $\Psi \left[\varphi \left(x\right)\right]=3^{x^2+1}.$
• B. $\varphi \left[\Psi \left[x\right]\right]=3^{2x}+1$
• C. $\Psi \left[\varphi \left(x\right)\right]=3^{x^3+1}.$
• D. $\varphi \left[\Psi \left[x\right]\right]=3^x+1$

Answer 1

Answer: (A), (B)

The correct options are
A $\Psi \left[\varphi \left(x\right)\right]=3^{x^2+1}.$
B $\varphi \left[\Psi \left[x\right]\right]=3^{2x}+1$

$\varphi \left[\Psi \left[x\right]\right]=\varphi \left(3^x\right)={\left(3^x\right)}^2+1=3^{2x}+1$

and
$\Psi \left[\varphi \left(x\right)\right]=\Psi (x^2+1)=3^{x^2+1}.$