If (x) = x^2 + 1 and (x) = 3^x , then (x) and (x) = - Vidyadip

MCQ

If $\phi (x) = {x^2} + 1$ and $\psi (x) = {3^x}$, then $\phi \{ \psi (x)\} $ and $\psi \{ \phi (x)\} = $

A
${3^{2x + 1}},\;{3^{{x^2} + 1}}$
B
${3^{2x + 1}},\;{3^{{x^2}}} + 1$
✓
${3^{2x}} + 1,\;{3^{{x^2} + 1}}$
D
None of these

✓

Answer

Correct option: C.

${3^{2x}} + 1,\;{3^{{x^2} + 1}}$

c
(c) $\phi \,\left\{ {\psi \,(x)\,} \right\} = \phi \,({3^x}) = {({3^x})^2} + 1 = {3^{2x}} + 1$

and $\psi \,\left\{ {\phi \,(x)\,} \right\} = \psi \,({x^2} + 1) = {3^{{x^2} + 1}}$.

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