# Solving Equations

Exercise 1 1. Find the domain of each function (a) 8x + 3 = 4 + 8x (b) 7(x – 2) – 2x = 5x…

Exercise 1

1.

Find the domain of each function

(a) 8x + 3 = 4 + 8x

(b) 7(x – 2) – 2x = 5x – 14

(c) 12 + 4x = –2(2x – 6) (e) 12 + 4x = –2(2x – 6)

Exercise 3

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3−2𝑥 (𝑎)𝑓(𝑥) = 2𝑥2−3𝑥

(𝑏)𝑓(𝑥) = √|𝑥| (𝑐)𝑓(𝑥) = √𝑥2 − 9 (𝑑)𝑓(𝑥) = √5 − 𝑥2

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(𝑒)𝑓(𝑥) = √𝑥 − 4𝑥 − 5……………………..

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Let f be a function defined by𝑓(𝑥) = (𝑥 − 2) function f.

,𝑥 ≥ 2. Find the inverse of the …………………………………………………………………………………………

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The function 𝑓(𝑥) = |𝑥| is invertible on R (i.e. admits an inverse)? Explain. …………………………………………………………………………………………

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Exercise 2

Determine if the equation has one solution, no solution or infinitely many solutions.

Solve each equation or inequality for x. Plot your solution on a number line

(𝑥−3)2=494(2𝑥−3)+5=93𝑥–5>16 4. −(𝑥+5)≤3𝑥(𝑥2−2)≥0

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Exercise 4

Solve each equation or inequality

2𝑥2−𝑥=−3

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2𝑥2−𝑥<−3 …………………………………………………………………………………………

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𝑥75

= − 𝑥2 2𝑥2

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𝑥+2=2√2𝑥−7 …………………………………………………………………………………………

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Exercise 5

Solve the systems

{4𝑥−3𝑦−2=3𝑥−7𝑦}

𝑥 + 5𝑦 − 2 = 𝑦 + 4

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2𝑥 + 𝑦 + 6𝑧 = 3

{ 𝑥−𝑦+4𝑧=1 }

3𝑥 + 2𝑦 − 2𝑧 = 2

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Exercise 6

A person invested \$ 120,000, part at an interest rate at 4% annually and the remainder at 5% annually. The total interest at the end of one year was equivalent to an annual 4.5% rate on the entire \$ 120,000. How much was invested at each rate.

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Exercise 7

The Davis company manufactures a product that has a unit selling prices of \$20 and a unit cost of \$15. If fixed costs are \$600,000, determine the least number of units that must be sold for the company to have a profit.

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Sample Solution