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Math  /  Algebra

Question4.) f(x)=2x−79x+1f(x)=\frac{2 x-7}{9 x+1}

Studdy Solution

STEP 1

1. The function f(x)=2x−79x+1 f(x) = \frac{2x - 7}{9x + 1} is a rational function.
2. The domain of a rational function is all real numbers except where the denominator is zero.

STEP 2

1. Identify the denominator of the function.
2. Determine where the denominator is equal to zero.
3. Exclude these values from the domain.

STEP 3

Identify the denominator of the function f(x)=2x−79x+1 f(x) = \frac{2x - 7}{9x + 1} .
The denominator is:
9x+1 9x + 1

STEP 4

Determine where the denominator is equal to zero by solving the equation:
9x+1=0 9x + 1 = 0

STEP 5

Solve the equation 9x+1=0 9x + 1 = 0 for x x :
Subtract 1 from both sides:
9x=−1 9x = -1
Divide both sides by 9:
x=−19 x = -\frac{1}{9}

STEP 6

Exclude the value x=−19 x = -\frac{1}{9} from the domain of the function. Therefore, the domain of f(x) f(x) is all real numbers except x=−19 x = -\frac{1}{9} .
The domain of the function is all real numbers except x=−19 x = -\frac{1}{9} .

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