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Chapter 10: Q89. (page 530)

Find $g [h (x)] 鈥� and h [g (x)]$ for the functions $h (x) = 2 x + 5 and g (x) = - x + 3$ .

Short Answer

Expert verified

The value of $g [h (x)] = - 2 x - 2 and h [g (x)] = - 2 x + 11$ .

Step by step solution

01

Step 1. Write down the given equation.

The given functions are $h (x) = 2 x + 5 and g (x) = - x + 3$ .

02

Step 2. Evaluating ghx and hgx.

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

$\begin{matrix} g (x) = 鈭� x + 3.... (Given) \\ g [h (x)] = 鈭� [h (x)] + 3.... (Plugging x = h (x)) \\ g [h (x)] = 鈭� [2 x + 5] + 3.... (鈭� h (x) = 2 x + 5) \\ g [h (x)] = 鈭� 2 x 鈭� 2 \\ Now, h (x) = 2 x + 5.... (Given) \\ h [g (x)] = 2 [g (x)] + 5.... (Plugging x = g (x)) \\ h [g (x)] = 2 (鈭� x + 3) + 5.... (鈭� g (x) = 鈭� x + 3) \\ h [g (x)] = 鈭� 2 x + 11 \end{matrix}$

03

Step 3. Conclusion.

The value of $g [h (x)] = - 2 x - 2 and h [g (x)] = - 2 x + 11$ .

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