# How do you find the domain of #f(x)=x/(6x^2+13x-5)#?

Domain (value of x) is any real value except

By signing up, you agree to our Terms of Service and Privacy Policy

To find the domain of ( f(x) = \frac{x}{6x^2 + 13x - 5} ), we need to determine the values of ( x ) for which the function is defined. The function will be undefined if the denominator equals zero because division by zero is undefined in mathematics. Therefore, we set the denominator equal to zero and solve for ( x ) to find any values that make the function undefined.

The denominator ( 6x^2 + 13x - 5 ) can be factored as ( (2x - 1)(3x + 5) ).

Setting the denominator equal to zero: [ 6x^2 + 13x - 5 = 0 ]

Factoring: [ (2x - 1)(3x + 5) = 0 ]

Setting each factor equal to zero and solving for ( x ): [ 2x - 1 = 0 \Rightarrow x = \frac{1}{2} ] [ 3x + 5 = 0 \Rightarrow x = -\frac{5}{3} ]

Therefore, the domain of ( f(x) ) is all real numbers except ( x = \frac{1}{2} ) and ( x = -\frac{5}{3} ). In interval notation, the domain is ( (-\infty, -\frac{5}{3}) \cup (-\frac{5}{3}, \frac{1}{2}) \cup (\frac{1}{2}, \infty) ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the domain and range of #f(x) = -sqrt(2x + 4) + 3#?
- What is the value of the algebraic expression #4x^2y-2xy^2+y# if #x=1# and #y=-4#?
- A jeweler has five rings, each weighing 18g, made of 5% silver and 95% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 75%. How much silver should he add?
- How do you find the domain and range of #Y=-x^2+4x-1#?
- How do you find the domain of the function #f(x)= -x^2 + 2x +3#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7