Suppose that the functions g and f are defined as follows.

Question

g(x)=−5+3x²

f(x)=7-6x

(a) Find (g/f)(−2)

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(b) Find all values that are NOT in the domain of g/f

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If there is more than one value, separate them with commas.

Answer 1

Hi Quinton

g(x)=−5+3x²

f(x)=7-6x

(a) Find (g/f)(−2)

(g/f)(x)= (-5+3x²)/(7-6x)

(g/f)(-2)= (-5 + (-2)²)/(7-6(-2)) = (-5+4)/(7+12) = 1/19

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(b) Find all values that are NOT in the domain of g/f

To avoid division by zero, 7 - 6x can't equal zero. So, 7 - 6x ≠ 0, then 7 ≠ 6x, then 7/6 ≠ x

So the domain of x all real numbers except 7/6

Enjoy