If the function f : R R be given by f(x) = x^2 + 2 and g : R R is… - Vidyadip

MCQ

If the function $f : R \rightarrow R$ be given by $ \text{f}(\text{x}) = \text{x}^2 + 2$ and $g : R \rightarrow R$ is given by $\text{g}(\text{x})=\frac{\text{x}}{\text{ x - 1}}$ The value of $gof(x)$ is.

✓
$ \frac{(\text{x}^{2} + 2)}{(\text{x}^{2} + 1)}$
B
$ \frac{\text{x}^{2}}{(\text{x}^{2} + 1)}$
C
$ \frac{\text{x}^{ 2}}{(\text{x}^{2} + 2)}$
D
$ \text{None of these}$

✓

Answer

Correct option: A.

$ \frac{(\text{x}^{2} + 2)}{(\text{x}^{2} + 1)}$

Given $ \text{f}(\text{x}) = \text{x}^2 + 2$ and $\text{gof}(\text{x}) =\text{g}(\text{x}^{2} - 1)$
Now, $\text{gof}(\text{x}) =\text{g}(\text{x}^{2} + 2)$
$ = \frac{(\text{x}^{2} + 2)}{(\text{x}^{2} + 2 – 1)}$
$ = \frac{(\text{x}^{2} + 2)}{(\text{x}^{2} + 1)}$

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