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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 3: Q. 3.97 (page 323)

For the function $g (x) = 4 x - 7$ , evaluate the function.
$g (m^{2})$
$g (x - 3)$
localid="1644747294810" $g (x) - g (3)$

Short Answer

Expert verified

Part (a) $g (m^{2}) = 4 m^{2} - 7$

Part (b) $g (x - 3) = 4 x - 19$

Part (c) $g (x) - g (3) = 4 x - 12$

Step by step solution

01

Part (a) Step 1.

Substitute $x = m^{2}$ in localid="1644747562374" $g (x) = 4 x - 7$ ,

localid="1644747601123" $\begin{array}{rcl} g (m^{2}) & = & 4 (m^{2}) - 7 \\ = & 4 m^{2} - 7 \end{array}$

02

Part (b) Step 1.

Substitute $x - 3$ for $x$ in $g (x) = 4 x - 7$ ,

$\begin{array}{rcl} g (x - 3) & = & 4 (x - 3) - 7 \\ = & 4 x - 12 - 7 \\ = & 4 x - 19 \end{array}$

03

Part (c) Step 1.

$\begin{array}{rcl} g (x) - g (3) & = & (4 x - 7) - (4 (3) - 7) \\ = & 4 x - 7 - (12 - 7) \\ = & 4 x - 7 - 5 \\ = & 4 x - 12 \end{array}$

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