Chapter 8: Q. 14 (page 557)

Suppose that $f (x) = 4 x + 5 and g (x) = x^{2} + 5 x - 24$
(a) Solve $f (x) = 0$
(b) Solve $f (x) = 13$
(c) Solve $f (x) = g (x)$
(d) Solve $f (x) > 0$

Short Answer

Expert verified

The solution is

$(a) x = - \frac{5}{4} (b) x = 2 (c) x = \frac{- 1 \pm 3 \sqrt{13}}{2} (d) x \in (- \frac{5}{4}, \infty)$

Step by step solution

Part (a) Step 1. Given Information

We are given two functions,

$f (x) = 4 x + 5 and g (x) = x^{2} + 5 x - 24$

We need to find the solution of $f (x) = 0$

Part (a) Step 2, Solution of the equation

The given function is,

$f (x) = 4 x + 5$

For $f (x) = 0,$

$f (x) = 4 x + 5 = 0 4 x + 5 = 0 4 x = - 5 x = - \frac{5}{4}$

Part (b) Step 1. Solution of the equation

The given function is,

$f (x) = 4 x + 5 f o r f (x) = 13 4 x + 5 = 13 4 x = 13 - 5 4 x = 8 x = 2$

Part (c) Step 1. Solution of the equation

The given functions are, $f (x) = 4 x + 5 and g (x) = x^{2} + 5 x - 24$

For $f (x) = g (x)$

$4 x + 5 = x^{2} + 5 x - 24 x^{2} + x - 29 = 0 U \sin g x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}, = \frac{- 1 \pm \sqrt{1^{2} - 4 (1) (- 29)}}{2 (1)} = \frac{- 1 \pm \sqrt{1} + 116}{2} = \frac{- 1 \pm \sqrt{117}}{2} = \frac{- 1 \pm 3 \sqrt{13}}{2}$

Part (d) Step 1. Solution of the inequality

The given function is $f (x) = 4 x + 5$

For $f (x) > 0$

$f (x) = 4 x + 5 > 0 4 x + 5 > 0 4 x > - 5 x > - \frac{5}{4} x \in (- \frac{5}{4}, \infty)$

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Suppose that $f (x) = 4 x + 5 and g (x) = x^{2} + 5 x - 24$
(a) Solve $f (x) = 0$
(b) Solve $f (x) = 13$
(c) Solve $f (x) = g (x)$
(d) Solve $f (x) > 0$

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2, Solution of the equation

Part (b) Step 1. Solution of the equation

Part (c) Step 1. Solution of the equation

Part (d) Step 1. Solution of the inequality

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Suppose thatf(x)=4x+5andg(x)=x2+5x-24(a) Solvef(x)=0(b) Solvef(x)=13(c) Solvef(x)=g(x)(d) Solvef(x)>0

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2, Solution of the equation

Part (b) Step 1. Solution of the equation

Part (c) Step 1. Solution of the equation

Part (d) Step 1. Solution of the inequality

One App. One Place for Learning.

Most popular questions from this chapter

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Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Suppose that $f (x) = 4 x + 5 and g (x) = x^{2} + 5 x - 24$
(a) Solve $f (x) = 0$
(b) Solve $f (x) = 13$
(c) Solve $f (x) = g (x)$
(d) Solve $f (x) > 0$