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cannot understand these problems; find the domain of the function and express the answer in interval notation.

then explain in words or show work.

a) f(x) = 4x2 - 7x +3

b) g(x) = 10  over x+7

c)  f(x) = √4x - 16

d) g(x) = 2x over x-3

e) f(x) = 3x -9           

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1 Answer

Hello Char,

The domain is all the x-values, and the range is all the y-values.

a) f(x) = 4x2 - 7x +3

This is a polynomial. There are no denominators (so no division-by-zero) and no radicals (so no square-root-of-a-negative). There are no values that you can't plug in for x. When you have a polynomial, the answer is always the domain is "all x" or all real. Answer written in interval notation will be (-∞, +∞).

b) g(x) = 10 over x+7

The domain is all the values that x is allowed to take on. The only issue with this function is that you need to be careful not to divide by zero. So the only values that x can not take on are those which would cause division by zero. So ,set the denominator equal to zero and solve; your domain will be everything else.

set x + 7 = 0

         -7      -7


     x = -7 

The domain is "all x not equal to -7". Answer in interval notation will be (-∞, -7) U (-7, +∞)

c) f(x) = √4x - 16

The domain is all values that x can take on. The only issue with this function is that you cannot have a negative inside the square root. So , set the insides of radical sign greater-than-or-equal-to zero, and solve. The result will be the domain.

4x - 16 ≥ 0               (add 16 on both sides)

     16       16


4x ≥ 16

(4x/4) ≥ 16/4     (divide by 4 on both sides)

x ≥ 4

The domain is " all x ≥ 4". Answer in interval notation will be [4, +∞).

Problems d and e are same as b and a respectively.

I hope this helps you. If you've any questions you can ask me or any other tutor will be glad to help you.