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Chapter 10: Q88. (page 530)

Find $g [h (x)] 鈥� and h [g (x)]$ for the functions $h (x) = x + 3 and g (x) = x^{2}$ .

Short Answer

Expert verified

The value of $g [h (x)] = x^{2} + 6 x + 9 and h [g (x)] = x^{2} + 3$ .

Step by step solution

01

Step 1. Write down the given equation.

The given functions are $h (x) = x + 3 and g (x) = x^{2}$ .

02

Step 2. Evaluating ghx and hgx.

The value of $g [h (x)] and h [g (x)]$ is evaluated as:

$\begin{matrix} g (x) = x^{2} .... (Given) \\ g [h (x)] = {[h (x)]}^{2} .... (Plugging x = h (x)) \\ g [h (x)] = {(x + 3)}^{2} .... (鈭� h (x) = x + 3) \\ g [h (x)] = x^{2} + 6 x + 9 \\ Now, h (x) = x + 3.... (Given) \\ h [g (x)] = [g (x)] + 3.... (Plugging x = g (x)) \\ h [g (x)] = (x^{2}) + 3.... (鈭� g (x) = x^{2}) \\ h [g (x)] = x^{2} + 3 \end{matrix}$

03

Step 3. Conclusion.

The value of $g [h (x)] = x^{2} + 6 x + 9 and h [g (x)] = x^{2} + 3$

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